Conditions for Implicit-Degree Sum for Spanning Trees with Few Leaves in K1,4-Free Graphs Article Swipe
Junqing Cai
,
Cheng‐Kuan Lin
,
Qiang Sun
,
Panpan Wang
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3390/math11244981
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3390/math11244981
A graph with n vertices is called an n-graph. A spanning tree with at most k leaves is referred to as a spanning k-ended tree. Spanning k-ended trees are important in various fields such as network design, graph theory, and communication networks. They provide a structured way to connect all the nodes in a network while ensuring efficient communication and minimizing unnecessary connections. In addition, they serve as fundamental components for algorithms in routing, broadcasting, and spanning tree protocols. However, determining whether a connected graph has a spanning k-ended tree or not is NP-complete. Therefore, it is important to identify sufficient conditions for the existence of such trees. The implicit-degree proposed by Zhu, Li, and Deng is an important indicator for the Hamiltonian problem and the spanning k-ended tree problem. In this article, we provide two sufficient conditions for K1,4-free connected graphs to have spanning k-ended trees for k = 2, 3. We prove the following: Let G be a K1,4-free connected n-graph. For k = 2, 3, if the implicit-degree sum of any k + 1 independent vertices of G is at least n − k + 2, then G has a spanning k-ended tree. Moreover, we give two examples to show that the lower bounds n and n − 1 are the best possible.
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/math11244981
- OA Status
- gold
- Cited By
- 1
- References
- 17
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4389914601
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4389914601Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3390/math11244981Digital Object Identifier
- Title
-
Conditions for Implicit-Degree Sum for Spanning Trees with Few Leaves in K1,4-Free GraphsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-12-17Full publication date if available
- Authors
-
Junqing Cai, Cheng‐Kuan Lin, Qiang Sun, Panpan WangList of authors in order
- Landing page
-
https://doi.org/10.3390/math11244981Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.3390/math11244981Direct OA link when available
- Concepts
-
Spanning tree, Trémaux tree, Combinatorics, Connected dominating set, Minimum spanning tree, Minimum degree spanning tree, Mathematics, Discrete mathematics, Degree (music), Graph, Shortest-path tree, Connectivity, Kruskal's algorithm, Computer science, Line graph, Pathwidth, Physics, AcousticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2024: 1Per-year citation counts (last 5 years)
- References (count)
-
17Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4389914601 |
|---|---|
| doi | https://doi.org/10.3390/math11244981 |
| ids.doi | https://doi.org/10.3390/math11244981 |
| ids.openalex | https://openalex.org/W4389914601 |
| fwci | 0.43955229 |
| type | article |
| title | Conditions for Implicit-Degree Sum for Spanning Trees with Few Leaves in K1,4-Free Graphs |
| awards[0].id | https://openalex.org/G7988309589 |
| awards[0].funder_id | https://openalex.org/F4320321001 |
| awards[0].display_name | |
| awards[0].funder_award_id | 12371365 |
| awards[0].funder_display_name | National Natural Science Foundation of China |
| biblio.issue | 24 |
| biblio.volume | 11 |
| biblio.last_page | 4981 |
| biblio.first_page | 4981 |
| topics[0].id | https://openalex.org/T10829 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9998000264167786 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1705 |
| topics[0].subfield.display_name | Computer Networks and Communications |
| topics[0].display_name | Interconnection Networks and Systems |
| topics[1].id | https://openalex.org/T10374 |
| topics[1].field.id | https://openalex.org/fields/17 |
| topics[1].field.display_name | Computer Science |
| topics[1].score | 0.9994999766349792 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1703 |
| topics[1].subfield.display_name | Computational Theory and Mathematics |
| topics[1].display_name | Advanced Graph Theory Research |
| topics[2].id | https://openalex.org/T12541 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.9962000250816345 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1703 |
| topics[2].subfield.display_name | Computational Theory and Mathematics |
| topics[2].display_name | Graph Labeling and Dimension Problems |
| funders[0].id | https://openalex.org/F4320321001 |
| funders[0].ror | https://ror.org/01h0zpd94 |
| funders[0].display_name | National Natural Science Foundation of China |
| is_xpac | False |
| apc_list.value | 1800 |
| apc_list.currency | CHF |
| apc_list.value_usd | 1949 |
| apc_paid.value | 1800 |
| apc_paid.currency | CHF |
| apc_paid.value_usd | 1949 |
| concepts[0].id | https://openalex.org/C64331007 |
| concepts[0].level | 2 |
| concepts[0].score | 0.9126810431480408 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q831672 |
| concepts[0].display_name | Spanning tree |
| concepts[1].id | https://openalex.org/C124302570 |
| concepts[1].level | 5 |
| concepts[1].score | 0.7383349537849426 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q7849146 |
| concepts[1].display_name | Trémaux tree |
| concepts[2].id | https://openalex.org/C114614502 |
| concepts[2].level | 1 |
| concepts[2].score | 0.7089318037033081 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q76592 |
| concepts[2].display_name | Combinatorics |
| concepts[3].id | https://openalex.org/C37810922 |
| concepts[3].level | 3 |
| concepts[3].score | 0.6817159652709961 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q5161409 |
| concepts[3].display_name | Connected dominating set |
| concepts[4].id | https://openalex.org/C13743678 |
| concepts[4].level | 2 |
| concepts[4].score | 0.678084671497345 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q240464 |
| concepts[4].display_name | Minimum spanning tree |
| concepts[5].id | https://openalex.org/C64271015 |
| concepts[5].level | 3 |
| concepts[5].score | 0.6489753127098083 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q6865444 |
| concepts[5].display_name | Minimum degree spanning tree |
| concepts[6].id | https://openalex.org/C33923547 |
| concepts[6].level | 0 |
| concepts[6].score | 0.5495110154151917 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[6].display_name | Mathematics |
| concepts[7].id | https://openalex.org/C118615104 |
| concepts[7].level | 1 |
| concepts[7].score | 0.48053011298179626 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q121416 |
| concepts[7].display_name | Discrete mathematics |
| concepts[8].id | https://openalex.org/C2775997480 |
| concepts[8].level | 2 |
| concepts[8].score | 0.4650702476501465 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q586277 |
| concepts[8].display_name | Degree (music) |
| concepts[9].id | https://openalex.org/C132525143 |
| concepts[9].level | 2 |
| concepts[9].score | 0.4429887533187866 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q141488 |
| concepts[9].display_name | Graph |
| concepts[10].id | https://openalex.org/C23394520 |
| concepts[10].level | 3 |
| concepts[10].score | 0.44061288237571716 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q4919350 |
| concepts[10].display_name | Shortest-path tree |
| concepts[11].id | https://openalex.org/C76444178 |
| concepts[11].level | 3 |
| concepts[11].score | 0.4274926483631134 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q72897900 |
| concepts[11].display_name | Connectivity |
| concepts[12].id | https://openalex.org/C63645285 |
| concepts[12].level | 3 |
| concepts[12].score | 0.41515329480171204 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q797860 |
| concepts[12].display_name | Kruskal's algorithm |
| concepts[13].id | https://openalex.org/C41008148 |
| concepts[13].level | 0 |
| concepts[13].score | 0.3395461440086365 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[13].display_name | Computer science |
| concepts[14].id | https://openalex.org/C203776342 |
| concepts[14].level | 3 |
| concepts[14].score | 0.21936950087547302 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q1378376 |
| concepts[14].display_name | Line graph |
| concepts[15].id | https://openalex.org/C43517604 |
| concepts[15].level | 4 |
| concepts[15].score | 0.14631545543670654 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q7144893 |
| concepts[15].display_name | Pathwidth |
| concepts[16].id | https://openalex.org/C121332964 |
| concepts[16].level | 0 |
| concepts[16].score | 0.053511232137680054 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[16].display_name | Physics |
| concepts[17].id | https://openalex.org/C24890656 |
| concepts[17].level | 1 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q82811 |
| concepts[17].display_name | Acoustics |
| keywords[0].id | https://openalex.org/keywords/spanning-tree |
| keywords[0].score | 0.9126810431480408 |
| keywords[0].display_name | Spanning tree |
| keywords[1].id | https://openalex.org/keywords/trémaux-tree |
| keywords[1].score | 0.7383349537849426 |
| keywords[1].display_name | Trémaux tree |
| keywords[2].id | https://openalex.org/keywords/combinatorics |
| keywords[2].score | 0.7089318037033081 |
| keywords[2].display_name | Combinatorics |
| keywords[3].id | https://openalex.org/keywords/connected-dominating-set |
| keywords[3].score | 0.6817159652709961 |
| keywords[3].display_name | Connected dominating set |
| keywords[4].id | https://openalex.org/keywords/minimum-spanning-tree |
| keywords[4].score | 0.678084671497345 |
| keywords[4].display_name | Minimum spanning tree |
| keywords[5].id | https://openalex.org/keywords/minimum-degree-spanning-tree |
| keywords[5].score | 0.6489753127098083 |
| keywords[5].display_name | Minimum degree spanning tree |
| keywords[6].id | https://openalex.org/keywords/mathematics |
| keywords[6].score | 0.5495110154151917 |
| keywords[6].display_name | Mathematics |
| keywords[7].id | https://openalex.org/keywords/discrete-mathematics |
| keywords[7].score | 0.48053011298179626 |
| keywords[7].display_name | Discrete mathematics |
| keywords[8].id | https://openalex.org/keywords/degree |
| keywords[8].score | 0.4650702476501465 |
| keywords[8].display_name | Degree (music) |
| keywords[9].id | https://openalex.org/keywords/graph |
| keywords[9].score | 0.4429887533187866 |
| keywords[9].display_name | Graph |
| keywords[10].id | https://openalex.org/keywords/shortest-path-tree |
| keywords[10].score | 0.44061288237571716 |
| keywords[10].display_name | Shortest-path tree |
| keywords[11].id | https://openalex.org/keywords/connectivity |
| keywords[11].score | 0.4274926483631134 |
| keywords[11].display_name | Connectivity |
| keywords[12].id | https://openalex.org/keywords/kruskals-algorithm |
| keywords[12].score | 0.41515329480171204 |
| keywords[12].display_name | Kruskal's algorithm |
| keywords[13].id | https://openalex.org/keywords/computer-science |
| keywords[13].score | 0.3395461440086365 |
| keywords[13].display_name | Computer science |
| keywords[14].id | https://openalex.org/keywords/line-graph |
| keywords[14].score | 0.21936950087547302 |
| keywords[14].display_name | Line graph |
| keywords[15].id | https://openalex.org/keywords/pathwidth |
| keywords[15].score | 0.14631545543670654 |
| keywords[15].display_name | Pathwidth |
| keywords[16].id | https://openalex.org/keywords/physics |
| keywords[16].score | 0.053511232137680054 |
| keywords[16].display_name | Physics |
| language | en |
| locations[0].id | doi:10.3390/math11244981 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4210192031 |
| locations[0].source.issn | 2227-7390 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2227-7390 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | Mathematics |
| locations[0].source.host_organization | https://openalex.org/P4310310987 |
| locations[0].source.host_organization_name | Multidisciplinary Digital Publishing Institute |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310310987 |
| locations[0].source.host_organization_lineage_names | Multidisciplinary Digital Publishing Institute |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Mathematics |
| locations[0].landing_page_url | https://doi.org/10.3390/math11244981 |
| locations[1].id | pmh:oai:doaj.org/article:6c0c26ae9eb34f5487bc0830f8c117c0 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306401280 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | DOAJ (DOAJ: Directory of Open Access Journals) |
| locations[1].source.host_organization | |
| locations[1].source.host_organization_name | |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | article |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | Mathematics, Vol 11, Iss 24, p 4981 (2023) |
| locations[1].landing_page_url | https://doaj.org/article/6c0c26ae9eb34f5487bc0830f8c117c0 |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5019857718 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-2070-8845 |
| authorships[0].author.display_name | Junqing Cai |
| authorships[0].countries | CN |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I15062923 |
| authorships[0].affiliations[0].raw_affiliation_string | School of Mathematical Science, Tianjin Normal University, Tianjin 300387, China |
| authorships[0].institutions[0].id | https://openalex.org/I15062923 |
| authorships[0].institutions[0].ror | https://ror.org/05x2td559 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I15062923 |
| authorships[0].institutions[0].country_code | CN |
| authorships[0].institutions[0].display_name | Tianjin Normal University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Junqing Cai |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | School of Mathematical Science, Tianjin Normal University, Tianjin 300387, China |
| authorships[1].author.id | https://openalex.org/A5070012673 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-2056-3690 |
| authorships[1].author.display_name | Cheng‐Kuan Lin |
| authorships[1].countries | TW |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I148366613 |
| authorships[1].affiliations[0].raw_affiliation_string | Department of Computer Science, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan |
| authorships[1].institutions[0].id | https://openalex.org/I148366613 |
| authorships[1].institutions[0].ror | https://ror.org/00se2k293 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I148366613 |
| authorships[1].institutions[0].country_code | TW |
| authorships[1].institutions[0].display_name | National Yang Ming Chiao Tung University |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Cheng-Kuan Lin |
| authorships[1].is_corresponding | True |
| authorships[1].raw_affiliation_strings | Department of Computer Science, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan |
| authorships[2].author.id | https://openalex.org/A5114803547 |
| authorships[2].author.orcid | https://orcid.org/0000-0002-5073-8519 |
| authorships[2].author.display_name | Qiang Sun |
| authorships[2].countries | CN |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I78978612 |
| authorships[2].affiliations[0].raw_affiliation_string | School of Mathematical Science, Yangzhou University, Yangzhou 225009, China |
| authorships[2].institutions[0].id | https://openalex.org/I78978612 |
| authorships[2].institutions[0].ror | https://ror.org/03tqb8s11 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I78978612 |
| authorships[2].institutions[0].country_code | CN |
| authorships[2].institutions[0].display_name | Yangzhou University |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Qiang Sun |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | School of Mathematical Science, Yangzhou University, Yangzhou 225009, China |
| authorships[3].author.id | https://openalex.org/A5047410302 |
| authorships[3].author.orcid | https://orcid.org/0000-0002-6664-2546 |
| authorships[3].author.display_name | Panpan Wang |
| authorships[3].countries | CN |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I125839683 |
| authorships[3].affiliations[0].raw_affiliation_string | School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China |
| authorships[3].institutions[0].id | https://openalex.org/I125839683 |
| authorships[3].institutions[0].ror | https://ror.org/01skt4w74 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I125839683, https://openalex.org/I890469752 |
| authorships[3].institutions[0].country_code | CN |
| authorships[3].institutions[0].display_name | Beijing Institute of Technology |
| authorships[3].author_position | last |
| authorships[3].raw_author_name | Panpan Wang |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.3390/math11244981 |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2023-12-19T00:00:00 |
| display_name | Conditions for Implicit-Degree Sum for Spanning Trees with Few Leaves in K1,4-Free Graphs |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10829 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9998000264167786 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1705 |
| primary_topic.subfield.display_name | Computer Networks and Communications |
| primary_topic.display_name | Interconnection Networks and Systems |
| related_works | https://openalex.org/W2014991506, https://openalex.org/W2779648845, https://openalex.org/W2307044859, https://openalex.org/W4380840098, https://openalex.org/W2138987445, https://openalex.org/W2052473415, https://openalex.org/W2911818503, https://openalex.org/W1754127855, https://openalex.org/W4232108645, https://openalex.org/W2041080724 |
| cited_by_count | 1 |
| counts_by_year[0].year | 2024 |
| counts_by_year[0].cited_by_count | 1 |
| locations_count | 2 |
| best_oa_location.id | doi:10.3390/math11244981 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4210192031 |
| best_oa_location.source.issn | 2227-7390 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2227-7390 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | Mathematics |
| best_oa_location.source.host_organization | https://openalex.org/P4310310987 |
| best_oa_location.source.host_organization_name | Multidisciplinary Digital Publishing Institute |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310310987 |
| best_oa_location.source.host_organization_lineage_names | Multidisciplinary Digital Publishing Institute |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Mathematics |
| best_oa_location.landing_page_url | https://doi.org/10.3390/math11244981 |
| primary_location.id | doi:10.3390/math11244981 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4210192031 |
| primary_location.source.issn | 2227-7390 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2227-7390 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | Mathematics |
| primary_location.source.host_organization | https://openalex.org/P4310310987 |
| primary_location.source.host_organization_name | Multidisciplinary Digital Publishing Institute |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310310987 |
| primary_location.source.host_organization_lineage_names | Multidisciplinary Digital Publishing Institute |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Mathematics |
| primary_location.landing_page_url | https://doi.org/10.3390/math11244981 |
| publication_date | 2023-12-17 |
| publication_year | 2023 |
| referenced_works | https://openalex.org/W4232896595, https://openalex.org/W1966931974, https://openalex.org/W4239638204, https://openalex.org/W2290059144, https://openalex.org/W2963417777, https://openalex.org/W2965216116, https://openalex.org/W2058894268, https://openalex.org/W3151068473, https://openalex.org/W2017852713, https://openalex.org/W2084408260, https://openalex.org/W1992714766, https://openalex.org/W4213185651, https://openalex.org/W2033687719, https://openalex.org/W2317857145, https://openalex.org/W2565029142, https://openalex.org/W2094970300, https://openalex.org/W2608652533 |
| referenced_works_count | 17 |
| abstract_inverted_index.+ | 175, 187 |
| abstract_inverted_index.1 | 176, 211 |
| abstract_inverted_index.= | 149, 165 |
| abstract_inverted_index.A | 0, 9 |
| abstract_inverted_index.G | 157, 180, 190 |
| abstract_inverted_index.a | 21, 44, 53, 82, 86, 159, 192 |
| abstract_inverted_index.k | 15, 148, 164, 174, 186 |
| abstract_inverted_index.n | 3, 184, 207, 209 |
| abstract_inverted_index.2, | 150, 166, 188 |
| abstract_inverted_index.3, | 167 |
| abstract_inverted_index.3. | 151 |
| abstract_inverted_index.In | 63, 130 |
| abstract_inverted_index.We | 152 |
| abstract_inverted_index.an | 7, 117 |
| abstract_inverted_index.as | 20, 34, 67 |
| abstract_inverted_index.at | 13, 182 |
| abstract_inverted_index.be | 158 |
| abstract_inverted_index.by | 111 |
| abstract_inverted_index.if | 168 |
| abstract_inverted_index.in | 30, 52, 72 |
| abstract_inverted_index.is | 5, 17, 92, 96, 116, 181 |
| abstract_inverted_index.it | 95 |
| abstract_inverted_index.of | 105, 172, 179 |
| abstract_inverted_index.or | 90 |
| abstract_inverted_index.to | 19, 47, 98, 142, 201 |
| abstract_inverted_index.we | 133, 197 |
| abstract_inverted_index.For | 163 |
| abstract_inverted_index.Let | 156 |
| abstract_inverted_index.Li, | 113 |
| abstract_inverted_index.The | 108 |
| abstract_inverted_index.all | 49 |
| abstract_inverted_index.and | 39, 59, 75, 114, 124, 208 |
| abstract_inverted_index.any | 173 |
| abstract_inverted_index.are | 28, 212 |
| abstract_inverted_index.for | 70, 102, 120, 138, 147 |
| abstract_inverted_index.has | 85, 191 |
| abstract_inverted_index.not | 91 |
| abstract_inverted_index.sum | 171 |
| abstract_inverted_index.the | 50, 103, 121, 125, 154, 169, 204, 213 |
| abstract_inverted_index.two | 135, 199 |
| abstract_inverted_index.way | 46 |
| abstract_inverted_index.− | 185, 210 |
| abstract_inverted_index.Deng | 115 |
| abstract_inverted_index.They | 42 |
| abstract_inverted_index.Zhu, | 112 |
| abstract_inverted_index.best | 214 |
| abstract_inverted_index.give | 198 |
| abstract_inverted_index.have | 143 |
| abstract_inverted_index.most | 14 |
| abstract_inverted_index.show | 202 |
| abstract_inverted_index.such | 33, 106 |
| abstract_inverted_index.that | 203 |
| abstract_inverted_index.then | 189 |
| abstract_inverted_index.they | 65 |
| abstract_inverted_index.this | 131 |
| abstract_inverted_index.tree | 11, 77, 89, 128 |
| abstract_inverted_index.with | 2, 12 |
| abstract_inverted_index.graph | 1, 37, 84 |
| abstract_inverted_index.least | 183 |
| abstract_inverted_index.lower | 205 |
| abstract_inverted_index.nodes | 51 |
| abstract_inverted_index.prove | 153 |
| abstract_inverted_index.serve | 66 |
| abstract_inverted_index.tree. | 24, 195 |
| abstract_inverted_index.trees | 27, 146 |
| abstract_inverted_index.while | 55 |
| abstract_inverted_index.bounds | 206 |
| abstract_inverted_index.called | 6 |
| abstract_inverted_index.fields | 32 |
| abstract_inverted_index.graphs | 141 |
| abstract_inverted_index.leaves | 16 |
| abstract_inverted_index.trees. | 107 |
| abstract_inverted_index.connect | 48 |
| abstract_inverted_index.design, | 36 |
| abstract_inverted_index.k-ended | 23, 26, 88, 127, 145, 194 |
| abstract_inverted_index.network | 35, 54 |
| abstract_inverted_index.problem | 123 |
| abstract_inverted_index.provide | 43, 134 |
| abstract_inverted_index.theory, | 38 |
| abstract_inverted_index.various | 31 |
| abstract_inverted_index.whether | 81 |
| abstract_inverted_index.However, | 79 |
| abstract_inverted_index.Spanning | 25 |
| abstract_inverted_index.article, | 132 |
| abstract_inverted_index.ensuring | 56 |
| abstract_inverted_index.examples | 200 |
| abstract_inverted_index.identify | 99 |
| abstract_inverted_index.n-graph. | 8, 162 |
| abstract_inverted_index.problem. | 129 |
| abstract_inverted_index.proposed | 110 |
| abstract_inverted_index.referred | 18 |
| abstract_inverted_index.routing, | 73 |
| abstract_inverted_index.spanning | 10, 22, 76, 87, 126, 144, 193 |
| abstract_inverted_index.vertices | 4, 178 |
| abstract_inverted_index.K1,4-free | 139, 160 |
| abstract_inverted_index.Moreover, | 196 |
| abstract_inverted_index.addition, | 64 |
| abstract_inverted_index.connected | 83, 140, 161 |
| abstract_inverted_index.efficient | 57 |
| abstract_inverted_index.existence | 104 |
| abstract_inverted_index.important | 29, 97, 118 |
| abstract_inverted_index.indicator | 119 |
| abstract_inverted_index.networks. | 41 |
| abstract_inverted_index.possible. | 215 |
| abstract_inverted_index.Therefore, | 94 |
| abstract_inverted_index.algorithms | 71 |
| abstract_inverted_index.components | 69 |
| abstract_inverted_index.conditions | 101, 137 |
| abstract_inverted_index.following: | 155 |
| abstract_inverted_index.minimizing | 60 |
| abstract_inverted_index.protocols. | 78 |
| abstract_inverted_index.structured | 45 |
| abstract_inverted_index.sufficient | 100, 136 |
| abstract_inverted_index.Hamiltonian | 122 |
| abstract_inverted_index.determining | 80 |
| abstract_inverted_index.fundamental | 68 |
| abstract_inverted_index.independent | 177 |
| abstract_inverted_index.unnecessary | 61 |
| abstract_inverted_index.NP-complete. | 93 |
| abstract_inverted_index.connections. | 62 |
| abstract_inverted_index.broadcasting, | 74 |
| abstract_inverted_index.communication | 40, 58 |
| abstract_inverted_index.implicit-degree | 109, 170 |
| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 90 |
| corresponding_author_ids | https://openalex.org/A5070012673 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 4 |
| corresponding_institution_ids | https://openalex.org/I148366613 |
| citation_normalized_percentile.value | 0.56621988 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |