Irregularity Strength of Circulant Graphs Using Algorithmic Approach Article Swipe
Muhammad Ahsan Asim
,
Roslan Hasni
,
Ali Ahmad
,
Basem Assiri
,
Andrea Semaničová–Feňovčíková
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1109/access.2021.3058786
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1109/access.2021.3058786
This paper deals with decomposition of complete graphs on vertices into circulant graphs with reduced degree . They are denoted as , where to are generators. Mathematical labeling for such bigger (higher order and huge size) and complex (strictly regular with so many triangles) graphs is very difficult. That is why after decomposition, an edge irregular -labeling for these subgraphs is computed with the help of algorithmic approach. Results of are computed by implementing this iterative algorithm in computer. Using the values of , an upper bound for edge irregularity strength is suggested for that is .
Related Topics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1109/access.2021.3058786
- https://ieeexplore.ieee.org/ielx7/6287639/9312710/09352734.pdf
- OA Status
- gold
- Cited By
- 3
- References
- 22
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3133142976
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W3133142976Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1109/access.2021.3058786Digital Object Identifier
- Title
-
Irregularity Strength of Circulant Graphs Using Algorithmic ApproachWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-01-01Full publication date if available
- Authors
-
Muhammad Ahsan Asim, Roslan Hasni, Ali Ahmad, Basem Assiri, Andrea Semaničová–FeňovčíkováList of authors in order
- Landing page
-
https://doi.org/10.1109/access.2021.3058786Publisher landing page
- PDF URL
-
https://ieeexplore.ieee.org/ielx7/6287639/9312710/09352734.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://ieeexplore.ieee.org/ielx7/6287639/9312710/09352734.pdfDirect OA link when available
- Concepts
-
Circulant matrix, Computer science, Theoretical computer science, AlgorithmTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
3Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2024: 1, 2022: 1Per-year citation counts (last 5 years)
- References (count)
-
22Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W3133142976 |
|---|---|
| doi | https://doi.org/10.1109/access.2021.3058786 |
| ids.doi | https://doi.org/10.1109/access.2021.3058786 |
| ids.mag | 3133142976 |
| ids.openalex | https://openalex.org/W3133142976 |
| fwci | 0.32018424 |
| type | article |
| title | Irregularity Strength of Circulant Graphs Using Algorithmic Approach |
| biblio.issue | |
| biblio.volume | 9 |
| biblio.last_page | 54406 |
| biblio.first_page | 54401 |
| topics[0].id | https://openalex.org/T12541 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9995999932289124 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1703 |
| topics[0].subfield.display_name | Computational Theory and Mathematics |
| topics[0].display_name | Graph Labeling and Dimension Problems |
| topics[1].id | https://openalex.org/T11476 |
| topics[1].field.id | https://openalex.org/fields/26 |
| topics[1].field.display_name | Mathematics |
| topics[1].score | 0.9987999796867371 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2608 |
| topics[1].subfield.display_name | Geometry and Topology |
| topics[1].display_name | Graph theory and applications |
| topics[2].id | https://openalex.org/T11797 |
| topics[2].field.id | https://openalex.org/fields/22 |
| topics[2].field.display_name | Engineering |
| topics[2].score | 0.9965999722480774 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2208 |
| topics[2].subfield.display_name | Electrical and Electronic Engineering |
| topics[2].display_name | graph theory and CDMA systems |
| is_xpac | False |
| apc_list.value | 1850 |
| apc_list.currency | USD |
| apc_list.value_usd | 1850 |
| apc_paid.value | 1850 |
| apc_paid.currency | USD |
| apc_paid.value_usd | 1850 |
| concepts[0].id | https://openalex.org/C115973184 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7946935296058655 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q245457 |
| concepts[0].display_name | Circulant matrix |
| concepts[1].id | https://openalex.org/C41008148 |
| concepts[1].level | 0 |
| concepts[1].score | 0.6139727830886841 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[1].display_name | Computer science |
| concepts[2].id | https://openalex.org/C80444323 |
| concepts[2].level | 1 |
| concepts[2].score | 0.3421629071235657 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q2878974 |
| concepts[2].display_name | Theoretical computer science |
| concepts[3].id | https://openalex.org/C11413529 |
| concepts[3].level | 1 |
| concepts[3].score | 0.2933805584907532 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q8366 |
| concepts[3].display_name | Algorithm |
| keywords[0].id | https://openalex.org/keywords/circulant-matrix |
| keywords[0].score | 0.7946935296058655 |
| keywords[0].display_name | Circulant matrix |
| keywords[1].id | https://openalex.org/keywords/computer-science |
| keywords[1].score | 0.6139727830886841 |
| keywords[1].display_name | Computer science |
| keywords[2].id | https://openalex.org/keywords/theoretical-computer-science |
| keywords[2].score | 0.3421629071235657 |
| keywords[2].display_name | Theoretical computer science |
| keywords[3].id | https://openalex.org/keywords/algorithm |
| keywords[3].score | 0.2933805584907532 |
| keywords[3].display_name | Algorithm |
| language | en |
| locations[0].id | doi:10.1109/access.2021.3058786 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S2485537415 |
| locations[0].source.issn | 2169-3536 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2169-3536 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | IEEE Access |
| locations[0].source.host_organization | https://openalex.org/P4310319808 |
| locations[0].source.host_organization_name | Institute of Electrical and Electronics Engineers |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310319808 |
| locations[0].source.host_organization_lineage_names | Institute of Electrical and Electronics Engineers |
| locations[0].license | cc-by |
| locations[0].pdf_url | https://ieeexplore.ieee.org/ielx7/6287639/9312710/09352734.pdf |
| 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 | IEEE Access |
| locations[0].landing_page_url | https://doi.org/10.1109/access.2021.3058786 |
| locations[1].id | pmh:oai:doaj.org/article:6b08bdcf26af43c18269105a009902f0 |
| locations[1].is_oa | True |
| 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 | cc-by-sa |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | article |
| locations[1].license_id | https://openalex.org/licenses/cc-by-sa |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | IEEE Access, Vol 9, Pp 54401-54406 (2021) |
| locations[1].landing_page_url | https://doaj.org/article/6b08bdcf26af43c18269105a009902f0 |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5034052727 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-4215-2825 |
| authorships[0].author.display_name | Muhammad Ahsan Asim |
| authorships[0].countries | SA |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I91450128 |
| authorships[0].affiliations[0].raw_affiliation_string | College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia |
| authorships[0].institutions[0].id | https://openalex.org/I91450128 |
| authorships[0].institutions[0].ror | https://ror.org/02bjnq803 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I91450128 |
| authorships[0].institutions[0].country_code | SA |
| authorships[0].institutions[0].display_name | Jazan University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Muhammad Ahsan Asim |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia |
| authorships[1].author.id | https://openalex.org/A5079555077 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-3695-2145 |
| authorships[1].author.display_name | Roslan Hasni |
| authorships[1].countries | MY |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I157696592 |
| authorships[1].affiliations[0].raw_affiliation_string | School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, Kuala Terengganu, Malaysia |
| authorships[1].institutions[0].id | https://openalex.org/I157696592 |
| authorships[1].institutions[0].ror | https://ror.org/02474f074 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I157696592 |
| authorships[1].institutions[0].country_code | MY |
| authorships[1].institutions[0].display_name | Universiti Malaysia Terengganu |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Roslan Hasni |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, Kuala Terengganu, Malaysia |
| authorships[2].author.id | https://openalex.org/A5101539889 |
| authorships[2].author.orcid | https://orcid.org/0000-0003-3434-9908 |
| authorships[2].author.display_name | Ali Ahmad |
| authorships[2].countries | SA |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I91450128 |
| authorships[2].affiliations[0].raw_affiliation_string | College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia |
| authorships[2].institutions[0].id | https://openalex.org/I91450128 |
| authorships[2].institutions[0].ror | https://ror.org/02bjnq803 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I91450128 |
| authorships[2].institutions[0].country_code | SA |
| authorships[2].institutions[0].display_name | Jazan University |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Ali Ahmad |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia |
| authorships[3].author.id | https://openalex.org/A5067688947 |
| authorships[3].author.orcid | https://orcid.org/0000-0002-4060-0655 |
| authorships[3].author.display_name | Basem Assiri |
| authorships[3].countries | SA |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I91450128 |
| authorships[3].affiliations[0].raw_affiliation_string | College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia |
| authorships[3].institutions[0].id | https://openalex.org/I91450128 |
| authorships[3].institutions[0].ror | https://ror.org/02bjnq803 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I91450128 |
| authorships[3].institutions[0].country_code | SA |
| authorships[3].institutions[0].display_name | Jazan University |
| authorships[3].author_position | middle |
| authorships[3].raw_author_name | Basem Assiri |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | College of Computer Science and Information Technology, Jazan University, Jazan, Saudi Arabia |
| authorships[4].author.id | https://openalex.org/A5033804594 |
| authorships[4].author.orcid | https://orcid.org/0000-0002-8432-9836 |
| authorships[4].author.display_name | Andrea Semaničová–Feňovčíková |
| authorships[4].countries | SK |
| authorships[4].affiliations[0].institution_ids | https://openalex.org/I183764125 |
| authorships[4].affiliations[0].raw_affiliation_string | Department of Applied Mathematics and Informatics, Technical University, Košice, Slovakia |
| authorships[4].institutions[0].id | https://openalex.org/I183764125 |
| authorships[4].institutions[0].ror | https://ror.org/05xm08015 |
| authorships[4].institutions[0].type | education |
| authorships[4].institutions[0].lineage | https://openalex.org/I183764125 |
| authorships[4].institutions[0].country_code | SK |
| authorships[4].institutions[0].display_name | Technical University of Košice |
| authorships[4].author_position | last |
| authorships[4].raw_author_name | Andrea Semanicova-Fenovcikova |
| authorships[4].is_corresponding | False |
| authorships[4].raw_affiliation_strings | Department of Applied Mathematics and Informatics, Technical University, Košice, Slovakia |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://ieeexplore.ieee.org/ielx7/6287639/9312710/09352734.pdf |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Irregularity Strength of Circulant Graphs Using Algorithmic Approach |
| has_fulltext | True |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T12541 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9995999932289124 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1703 |
| primary_topic.subfield.display_name | Computational Theory and Mathematics |
| primary_topic.display_name | Graph Labeling and Dimension Problems |
| related_works | https://openalex.org/W2748952813, https://openalex.org/W2117159910, https://openalex.org/W2139378013, https://openalex.org/W2044900700, https://openalex.org/W2560470131, https://openalex.org/W2049656902, https://openalex.org/W2394404719, https://openalex.org/W2903415888, https://openalex.org/W4287113494, https://openalex.org/W2348308003 |
| cited_by_count | 3 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 1 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 1 |
| counts_by_year[2].year | 2022 |
| counts_by_year[2].cited_by_count | 1 |
| locations_count | 2 |
| best_oa_location.id | doi:10.1109/access.2021.3058786 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S2485537415 |
| best_oa_location.source.issn | 2169-3536 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2169-3536 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | IEEE Access |
| best_oa_location.source.host_organization | https://openalex.org/P4310319808 |
| best_oa_location.source.host_organization_name | Institute of Electrical and Electronics Engineers |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310319808 |
| best_oa_location.source.host_organization_lineage_names | Institute of Electrical and Electronics Engineers |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | https://ieeexplore.ieee.org/ielx7/6287639/9312710/09352734.pdf |
| 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 | IEEE Access |
| best_oa_location.landing_page_url | https://doi.org/10.1109/access.2021.3058786 |
| primary_location.id | doi:10.1109/access.2021.3058786 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S2485537415 |
| primary_location.source.issn | 2169-3536 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2169-3536 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | IEEE Access |
| primary_location.source.host_organization | https://openalex.org/P4310319808 |
| primary_location.source.host_organization_name | Institute of Electrical and Electronics Engineers |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310319808 |
| primary_location.source.host_organization_lineage_names | Institute of Electrical and Electronics Engineers |
| primary_location.license | cc-by |
| primary_location.pdf_url | https://ieeexplore.ieee.org/ielx7/6287639/9312710/09352734.pdf |
| 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 | IEEE Access |
| primary_location.landing_page_url | https://doi.org/10.1109/access.2021.3058786 |
| publication_date | 2021-01-01 |
| publication_year | 2021 |
| referenced_works | https://openalex.org/W1965984179, https://openalex.org/W4246759618, https://openalex.org/W2039110949, https://openalex.org/W6685082242, https://openalex.org/W2342616878, https://openalex.org/W2048759904, https://openalex.org/W2950969150, https://openalex.org/W1910748354, https://openalex.org/W6760160266, https://openalex.org/W2094613978, https://openalex.org/W2074044667, https://openalex.org/W2003916665, https://openalex.org/W1970152983, https://openalex.org/W6759765478, https://openalex.org/W6775491472, https://openalex.org/W2753240036, https://openalex.org/W1881841366, https://openalex.org/W2168785519, https://openalex.org/W3013859425, https://openalex.org/W2918744402, https://openalex.org/W2919198524, https://openalex.org/W2018701924 |
| referenced_works_count | 22 |
| abstract_inverted_index.$ | 145 |
| abstract_inverted_index.an | 76, 117 |
| abstract_inverted_index.as | 28 |
| abstract_inverted_index.by | 102 |
| abstract_inverted_index.in | 107 |
| abstract_inverted_index.is | 68, 72, 86, 124, 136 |
| abstract_inverted_index.of | 5, 91, 95, 112 |
| abstract_inverted_index.on | 8 |
| abstract_inverted_index.so | 64 |
| abstract_inverted_index.to | 42 |
| abstract_inverted_index.}, | 34, 132 |
| abstract_inverted_index.and | 56, 59 |
| abstract_inverted_index.are | 26, 47, 100 |
| abstract_inverted_index.for | 51, 83, 120, 126 |
| abstract_inverted_index.the | 89, 110 |
| abstract_inverted_index.why | 73 |
| abstract_inverted_index.That | 71 |
| abstract_inverted_index.They | 25 |
| abstract_inverted_index.This | 0 |
| abstract_inverted_index._{2} | 142 |
| abstract_inverted_index.edge | 77, 121 |
| abstract_inverted_index.help | 90 |
| abstract_inverted_index.huge | 57 |
| abstract_inverted_index.into | 14 |
| abstract_inverted_index.many | 65 |
| abstract_inverted_index.n-1$ | 23 |
| abstract_inverted_index.such | 52 |
| abstract_inverted_index.that | 135 |
| abstract_inverted_index.this | 104 |
| abstract_inverted_index.very | 69 |
| abstract_inverted_index.with | 3, 17, 63, 88 |
| abstract_inverted_index.Using | 109 |
| abstract_inverted_index.\vert | 143 |
| abstract_inverted_index.after | 74 |
| abstract_inverted_index.bound | 119 |
| abstract_inverted_index.deals | 2 |
| abstract_inverted_index.order | 55 |
| abstract_inverted_index.paper | 1 |
| abstract_inverted_index.size) | 58 |
| abstract_inverted_index.these | 84 |
| abstract_inverted_index.upper | 118 |
| abstract_inverted_index.where | 37 |
| abstract_inverted_index.E\vert | 140 |
| abstract_inverted_index.V\vert | 144 |
| abstract_inverted_index.a_{2}, | 32, 130 |
| abstract_inverted_index.bigger | 53 |
| abstract_inverted_index.degree | 19 |
| abstract_inverted_index.graphs | 7, 16, 67 |
| abstract_inverted_index.values | 111 |
| abstract_inverted_index.{\dots | 33, 131 |
| abstract_inverted_index.(higher | 54 |
| abstract_inverted_index.Results | 94 |
| abstract_inverted_index.a_{m})$ | 35, 133 |
| abstract_inverted_index.complex | 60 |
| abstract_inverted_index.denoted | 27 |
| abstract_inverted_index.reduced | 18 |
| abstract_inverted_index.regular | 62 |
| abstract_inverted_index.complete | 6 |
| abstract_inverted_index.computed | 87, 101 |
| abstract_inverted_index.labeling | 50 |
| abstract_inverted_index.strength | 123 |
| abstract_inverted_index.vertices | 13 |
| abstract_inverted_index.(strictly | 61 |
| abstract_inverted_index.<tex-math | 10, 21, 30, 39, 44, 80, 97, 114, 128, 138 |
| abstract_inverted_index.algorithm | 106 |
| abstract_inverted_index.approach. | 93 |
| abstract_inverted_index.circulant | 15 |
| abstract_inverted_index.computer. | 108 |
| abstract_inverted_index.irregular | 78 |
| abstract_inverted_index.iterative | 105 |
| abstract_inverted_index.subgraphs | 85 |
| abstract_inverted_index.suggested | 125 |
| abstract_inverted_index.}/{2}\log | 141 |
| abstract_inverted_index.difficult. | 70 |
| abstract_inverted_index.triangles) | 66 |
| abstract_inverted_index.algorithmic | 92 |
| abstract_inverted_index.generators. | 48 |
| abstract_inverted_index.Mathematical | 49 |
| abstract_inverted_index.implementing | 103 |
| abstract_inverted_index.irregularity | 122 |
| abstract_inverted_index.decomposition | 4 |
| abstract_inverted_index.decomposition, | 75 |
| abstract_inverted_index.<inline-formula> | 9, 20, 29, 38, 43, 79, 96, 113, 127, 137 |
| abstract_inverted_index.notation="LaTeX">$k$ | 81, 98, 115 |
| abstract_inverted_index.notation="LaTeX">$n$ | 11 |
| abstract_inverted_index.notation="LaTeX">$r< | 22 |
| abstract_inverted_index.notation="LaTeX">$a_{1}$ | 40 |
| abstract_inverted_index.notation="LaTeX">$a_{m}$ | 45 |
| abstract_inverted_index.notation="LaTeX">${\vert | 139 |
| abstract_inverted_index.</tex-math></inline-formula> | 12, 41, 46, 99, 134 |
| abstract_inverted_index.</tex-math></inline-formula>, | 36, 116 |
| abstract_inverted_index.</tex-math></inline-formula>. | 24, 146 |
| abstract_inverted_index.notation="LaTeX">$C_{n}(a_{1}, | 31, 129 |
| abstract_inverted_index.</tex-math></inline-formula>-labeling | 82 |
| cited_by_percentile_year.max | 95 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 3 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile.value | 0.60005332 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |