Dominant Mixed Metric Dimension of Graph Article Swipe

View

Ridho Alfarisi , Sharifah Kartini Said Husain , Liliek Susilowati , Arika Indah Kristiana ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.19139/soic-2310-5070-1925

For $k-$ordered set $W=\{s_1, s_2,\dots, s_k \}$ of vertex set $G$, the representation of a vertex or edge $a$ of $G$ with respect to $W$ is $r(a|W)=(d(a,s_1), d(a,s_2),\dots, d(a,s_k))$ where $a$ is vertex so that $d(a,s_i)$ is a distance between of the vertex $v$ and the vertices in $W$ and $a=uv$ is edge so that $d(a,s_i)=min\{d(u,s_i),d(v,s_i)\}$. The set $W$ is a mixed resolving set of $G$ if $r(a|W)\neq r(b|W)$ for every pair $a,b$ of distinct vertices or edge of $G$. The minimum mixed resolving set $W$ is a mixed basis of $G$. If $G$ has a mixed basis, then its cardinality is called mixed metric dimension, denoted by $dim_m(G)$. A set $W$ of vertices in $G$ is a dominating set for $G$ if every vertex of $G$ that is not in $W$ is adjacent to some vertex of $W$. The minimum cardinality of dominating set is domination number , denoted by $\gamma(G)$. A vertex set of some vertices in $G$ that is both mixed resolving and dominating set is a mixed resolving dominating set. The minimum cardinality of mixed resolving dominating set is called dominant mixed metric dimension, denoted by $\gamma_{mr}(G)$. In our paper, we will investigated the establish sharp bounds of the dominant mixed metric dimension of $G$ and determine the exact value of some family graphs.

Related Topics

Mathematics

Performance Indicator

Combinatorics

Line Graph

Engineering

Operations Management

Concepts

Mathematics Dimension (graph theory) Graph Metric dimension Metric (unit) Combinatorics Line graph Engineering 1-planar graph Operations management

Metadata

Type: article
Language: en
Landing Page: https://doi.org/10.19139/soic-2310-5070-1925
OA Status: diamond
Cited By: 2
Related Works: 10
OpenAlex ID: https://openalex.org/W4403903153

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4403903153

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.19139/soic-2310-5070-1925

Digital Object Identifier
Title: Dominant Mixed Metric Dimension of Graph

Work title
Type: article

OpenAlex work type
Language: en

Primary language
Publication year: 2024

Year of publication
Publication date: 2024-06-21

Full publication date if available
Authors: Ridho Alfarisi, Sharifah Kartini Said Husain, Liliek Susilowati, Arika Indah Kristiana

List of authors in order
Landing page: https://doi.org/10.19139/soic-2310-5070-1925

Publisher landing page
Open access: Yes

Whether a free full text is available
OA status: diamond

Open access status per OpenAlex
OA URL: https://doi.org/10.19139/soic-2310-5070-1925

Direct OA link when available
Concepts: Mathematics, Dimension (graph theory), Graph, Metric dimension, Metric (unit), Combinatorics, Line graph, Engineering, 1-planar graph, Operations management

Top concepts (fields/topics) attached by OpenAlex
Cited by: 2

Total citation count in OpenAlex
Citations by year (recent): 2025: 2

Per-year citation counts (last 5 years)
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4403903153
doi	https://doi.org/10.19139/soic-2310-5070-1925
ids.doi	https://doi.org/10.19139/soic-2310-5070-1925
ids.openalex	https://openalex.org/W4403903153
fwci	1.58027115
type	article
title	Dominant Mixed Metric Dimension of Graph
biblio.issue	6
biblio.volume	12
biblio.last_page	1833
biblio.first_page	1826
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	0.9991000294685364
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/T12923
topics[1].field.id	https://openalex.org/fields/17
topics[1].field.display_name	Computer Science
topics[1].score	0.9700000286102295
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/1707
topics[1].subfield.display_name	Computer Vision and Pattern Recognition
topics[1].display_name	Digital Image Processing Techniques
topics[2].id	https://openalex.org/T11106
topics[2].field.id	https://openalex.org/fields/17
topics[2].field.display_name	Computer Science
topics[2].score	0.948199987411499
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/1711
topics[2].subfield.display_name	Signal Processing
topics[2].display_name	Data Management and Algorithms
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C33923547
concepts[0].level	0
concepts[0].score	0.5946967601776123
concepts[0].wikidata	https://www.wikidata.org/wiki/Q395
concepts[0].display_name	Mathematics
concepts[1].id	https://openalex.org/C33676613
concepts[1].level	2
concepts[1].score	0.5561726689338684
concepts[1].wikidata	https://www.wikidata.org/wiki/Q13415176
concepts[1].display_name	Dimension (graph theory)
concepts[2].id	https://openalex.org/C132525143
concepts[2].level	2
concepts[2].score	0.5192570686340332
concepts[2].wikidata	https://www.wikidata.org/wiki/Q141488
concepts[2].display_name	Graph
concepts[3].id	https://openalex.org/C60933471
concepts[3].level	5
concepts[3].score	0.48123788833618164
concepts[3].wikidata	https://www.wikidata.org/wiki/Q17152964
concepts[3].display_name	Metric dimension
concepts[4].id	https://openalex.org/C176217482
concepts[4].level	2
concepts[4].score	0.4750770926475525
concepts[4].wikidata	https://www.wikidata.org/wiki/Q860554
concepts[4].display_name	Metric (unit)
concepts[5].id	https://openalex.org/C114614502
concepts[5].level	1
concepts[5].score	0.4155062437057495
concepts[5].wikidata	https://www.wikidata.org/wiki/Q76592
concepts[5].display_name	Combinatorics
concepts[6].id	https://openalex.org/C203776342
concepts[6].level	3
concepts[6].score	0.21550631523132324
concepts[6].wikidata	https://www.wikidata.org/wiki/Q1378376
concepts[6].display_name	Line graph
concepts[7].id	https://openalex.org/C127413603
concepts[7].level	0
concepts[7].score	0.06517046689987183
concepts[7].wikidata	https://www.wikidata.org/wiki/Q11023
concepts[7].display_name	Engineering
concepts[8].id	https://openalex.org/C102192266
concepts[8].level	4
concepts[8].score	0.04640936851501465
concepts[8].wikidata	https://www.wikidata.org/wiki/Q4545823
concepts[8].display_name	1-planar graph
concepts[9].id	https://openalex.org/C21547014
concepts[9].level	1
concepts[9].score	0.0
concepts[9].wikidata	https://www.wikidata.org/wiki/Q1423657
concepts[9].display_name	Operations management
keywords[0].id	https://openalex.org/keywords/mathematics
keywords[0].score	0.5946967601776123
keywords[0].display_name	Mathematics
keywords[1].id	https://openalex.org/keywords/dimension
keywords[1].score	0.5561726689338684
keywords[1].display_name	Dimension (graph theory)
keywords[2].id	https://openalex.org/keywords/graph
keywords[2].score	0.5192570686340332
keywords[2].display_name	Graph
keywords[3].id	https://openalex.org/keywords/metric-dimension
keywords[3].score	0.48123788833618164
keywords[3].display_name	Metric dimension
keywords[4].id	https://openalex.org/keywords/metric
keywords[4].score	0.4750770926475525
keywords[4].display_name	Metric (unit)
keywords[5].id	https://openalex.org/keywords/combinatorics
keywords[5].score	0.4155062437057495
keywords[5].display_name	Combinatorics
keywords[6].id	https://openalex.org/keywords/line-graph
keywords[6].score	0.21550631523132324
keywords[6].display_name	Line graph
keywords[7].id	https://openalex.org/keywords/engineering
keywords[7].score	0.06517046689987183
keywords[7].display_name	Engineering
keywords[8].id	https://openalex.org/keywords/1-planar-graph
keywords[8].score	0.04640936851501465
keywords[8].display_name	1-planar graph
language	en
locations[0].id	doi:10.19139/soic-2310-5070-1925
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S2764412775
locations[0].source.issn	2310-5070, 2311-004X
locations[0].source.type	journal
locations[0].source.is_oa	True
locations[0].source.issn_l	2310-5070
locations[0].source.is_core	True
locations[0].source.is_in_doaj	False
locations[0].source.display_name	Statistics Optimization & Information Computing
locations[0].source.host_organization	https://openalex.org/P4310321236
locations[0].source.host_organization_name	International Academic Press
locations[0].source.host_organization_lineage	https://openalex.org/P4310321236
locations[0].source.host_organization_lineage_names	International Academic Press
locations[0].license
locations[0].pdf_url
locations[0].version	publishedVersion
locations[0].raw_type	journal-article
locations[0].license_id
locations[0].is_accepted	True
locations[0].is_published	True
locations[0].raw_source_name	Statistics, Optimization & Information Computing
locations[0].landing_page_url	https://doi.org/10.19139/soic-2310-5070-1925
locations[1].id	pmh:oai:ojs.localhost:article/1925
locations[1].is_oa	False
locations[1].source.id	https://openalex.org/S4306400041
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	VNU Journal of Science: Natural Sciences and Technology (Vietnam National University)
locations[1].source.host_organization	https://openalex.org/I177233841
locations[1].source.host_organization_name	Vietnam National University, Hanoi
locations[1].source.host_organization_lineage	https://openalex.org/I177233841
locations[1].license
locations[1].pdf_url
locations[1].version	publishedVersion
locations[1].raw_type	info:eu-repo/semantics/article
locations[1].license_id
locations[1].is_accepted	True
locations[1].is_published	True
locations[1].raw_source_name	Statistics, Optimization & Information Computing; Vol 12 No 6 (2024); 1826-1833
locations[1].landing_page_url	http://iapress.org/index.php/soic/article/view/1925
indexed_in	crossref
authorships[0].author.id	https://openalex.org/A5013391703
authorships[0].author.orcid	https://orcid.org/0000-0003-3011-4917
authorships[0].author.display_name	Ridho Alfarisi
authorships[0].author_position	first
authorships[0].raw_author_name	Ridho Alfarisi
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5071323071
authorships[1].author.orcid	https://orcid.org/0000-0001-5675-941X
authorships[1].author.display_name	Sharifah Kartini Said Husain
authorships[1].author_position	middle
authorships[1].raw_author_name	Sharifah Kartini Said Husain
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5069697914
authorships[2].author.orcid	https://orcid.org/0000-0002-9149-3570
authorships[2].author.display_name	Liliek Susilowati
authorships[2].author_position	middle
authorships[2].raw_author_name	Liliek Susilowati
authorships[2].is_corresponding	False
authorships[3].author.id	https://openalex.org/A5000682841
authorships[3].author.orcid	https://orcid.org/0000-0002-6556-6377
authorships[3].author.display_name	Arika Indah Kristiana
authorships[3].author_position	last
authorships[3].raw_author_name	Arika Indah Kristiana
authorships[3].is_corresponding	False
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://doi.org/10.19139/soic-2310-5070-1925
open_access.oa_status	diamond
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Dominant Mixed Metric Dimension of Graph
has_fulltext	False
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	0.9991000294685364
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/W4391375266, https://openalex.org/W2561539344, https://openalex.org/W1758702617, https://openalex.org/W2955893777, https://openalex.org/W2321819494, https://openalex.org/W3173364418, https://openalex.org/W4313448629, https://openalex.org/W4323310040, https://openalex.org/W3133002653, https://openalex.org/W2952616125
cited_by_count	2
counts_by_year[0].year	2025
counts_by_year[0].cited_by_count	2
locations_count	2
best_oa_location.id	doi:10.19139/soic-2310-5070-1925
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S2764412775
best_oa_location.source.issn	2310-5070, 2311-004X
best_oa_location.source.type	journal
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l	2310-5070
best_oa_location.source.is_core	True
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	Statistics Optimization & Information Computing
best_oa_location.source.host_organization	https://openalex.org/P4310321236
best_oa_location.source.host_organization_name	International Academic Press
best_oa_location.source.host_organization_lineage	https://openalex.org/P4310321236
best_oa_location.source.host_organization_lineage_names	International Academic Press
best_oa_location.license
best_oa_location.pdf_url
best_oa_location.version	publishedVersion
best_oa_location.raw_type	journal-article
best_oa_location.license_id
best_oa_location.is_accepted	True
best_oa_location.is_published	True
best_oa_location.raw_source_name	Statistics, Optimization & Information Computing
best_oa_location.landing_page_url	https://doi.org/10.19139/soic-2310-5070-1925
primary_location.id	doi:10.19139/soic-2310-5070-1925
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S2764412775
primary_location.source.issn	2310-5070, 2311-004X
primary_location.source.type	journal
primary_location.source.is_oa	True
primary_location.source.issn_l	2310-5070
primary_location.source.is_core	True
primary_location.source.is_in_doaj	False
primary_location.source.display_name	Statistics Optimization & Information Computing
primary_location.source.host_organization	https://openalex.org/P4310321236
primary_location.source.host_organization_name	International Academic Press
primary_location.source.host_organization_lineage	https://openalex.org/P4310321236
primary_location.source.host_organization_lineage_names	International Academic Press
primary_location.license
primary_location.pdf_url
primary_location.version	publishedVersion
primary_location.raw_type	journal-article
primary_location.license_id
primary_location.is_accepted	True
primary_location.is_published	True
primary_location.raw_source_name	Statistics, Optimization & Information Computing
primary_location.landing_page_url	https://doi.org/10.19139/soic-2310-5070-1925
publication_date	2024-06-21
publication_year	2024
referenced_works_count	0
abstract_inverted_index.,	148
abstract_inverted_index.A	109, 152
abstract_inverted_index.a	14, 37, 60, 87, 95, 117, 169
abstract_inverted_index.If	92
abstract_inverted_index.In	191
abstract_inverted_index.by	107, 150, 189
abstract_inverted_index.if	66, 122
abstract_inverted_index.in	47, 114, 130, 158
abstract_inverted_index.is	25, 31, 36, 51, 59, 86, 101, 116, 128, 132, 145, 161, 168, 182
abstract_inverted_index.of	7, 13, 19, 40, 64, 73, 78, 90, 112, 125, 137, 142, 155, 177, 201, 207, 214
abstract_inverted_index.or	16, 76
abstract_inverted_index.so	33, 53
abstract_inverted_index.to	23, 134
abstract_inverted_index.we	194
abstract_inverted_index.$G$	20, 65, 93, 115, 121, 126, 159, 208
abstract_inverted_index.$W$	24, 48, 58, 85, 111, 131
abstract_inverted_index.$a$	18, 30
abstract_inverted_index.$v$	43
abstract_inverted_index.For	0
abstract_inverted_index.The	56, 80, 139, 174
abstract_inverted_index.\}$	6
abstract_inverted_index.and	44, 49, 165, 209
abstract_inverted_index.for	69, 120
abstract_inverted_index.has	94
abstract_inverted_index.its	99
abstract_inverted_index.not	129
abstract_inverted_index.our	192
abstract_inverted_index.s_k	5
abstract_inverted_index.set	2, 9, 57, 63, 84, 110, 119, 144, 154, 167, 181
abstract_inverted_index.the	11, 41, 45, 197, 202, 211
abstract_inverted_index.$G$,	10
abstract_inverted_index.$G$.	79, 91
abstract_inverted_index.$W$.	138
abstract_inverted_index.both	162
abstract_inverted_index.edge	17, 52, 77
abstract_inverted_index.pair	71
abstract_inverted_index.set.	173
abstract_inverted_index.some	135, 156, 215
abstract_inverted_index.that	34, 54, 127, 160
abstract_inverted_index.then	98
abstract_inverted_index.will	195
abstract_inverted_index.with	21
abstract_inverted_index.$a,b$	72
abstract_inverted_index.basis	89
abstract_inverted_index.every	70, 123
abstract_inverted_index.exact	212
abstract_inverted_index.mixed	61, 82, 88, 96, 103, 163, 170, 178, 185, 204
abstract_inverted_index.sharp	199
abstract_inverted_index.value	213
abstract_inverted_index.where	29
abstract_inverted_index.$a=uv$	50
abstract_inverted_index.basis,	97
abstract_inverted_index.bounds	200
abstract_inverted_index.called	102, 183
abstract_inverted_index.family	216
abstract_inverted_index.metric	104, 186, 205
abstract_inverted_index.number	147
abstract_inverted_index.paper,	193
abstract_inverted_index.vertex	8, 15, 32, 42, 124, 136, 153
abstract_inverted_index.between	39
abstract_inverted_index.denoted	106, 149, 188
abstract_inverted_index.graphs.	217
abstract_inverted_index.minimum	81, 140, 175
abstract_inverted_index.r(b\|W)$	68
abstract_inverted_index.respect	22
abstract_inverted_index.adjacent	133
abstract_inverted_index.distance	38
abstract_inverted_index.distinct	74
abstract_inverted_index.dominant	184, 203
abstract_inverted_index.vertices	46, 75, 113, 157
abstract_inverted_index.$W=\{s_1,	3
abstract_inverted_index.determine	210
abstract_inverted_index.dimension	206
abstract_inverted_index.establish	198
abstract_inverted_index.resolving	62, 83, 164, 171, 179
abstract_inverted_index.$d(a,s_i)$	35
abstract_inverted_index.d(a,s_k))$	28
abstract_inverted_index.dimension,	105, 187
abstract_inverted_index.dominating	118, 143, 166, 172, 180
abstract_inverted_index.domination	146
abstract_inverted_index.s_2,\dots,	4
abstract_inverted_index.$dim_m(G)$.	108
abstract_inverted_index.$k-$ordered	1
abstract_inverted_index.$r(a\|W)\neq	67
abstract_inverted_index.cardinality	100, 141, 176
abstract_inverted_index.$\gamma(G)$.	151
abstract_inverted_index.investigated	196
abstract_inverted_index.representation	12
abstract_inverted_index.d(a,s_2),\dots,	27
abstract_inverted_index.$\gamma_{mr}(G)$.	190
abstract_inverted_index.$r(a\|W)=(d(a,s_1),	26
abstract_inverted_index.$d(a,s_i)=min\{d(u,s_i),d(v,s_i)\}$.	55
cited_by_percentile_year.max	97
cited_by_percentile_year.min	95
countries_distinct_count	0
institutions_distinct_count	4
citation_normalized_percentile.value	0.79694356
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False