Constant time calculation of the metric dimension of the join of path graphs

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dc.authorid0000-0002-5131-577X
dc.authorscopusid58119948300
dc.contributor.authorKhan, Asad ul Islam
dc.contributor.authorKhan, Asad ul Islam
dc.contributor.authorZhang, Chuanjun
dc.contributor.authorHaidar, Ghulam
dc.contributor.authorKhan, Murad ul Islam
dc.contributor.authorYousafzai, Faisal
dc.contributor.authorHila, Kostaq
dc.contributor.authorKhan, Asad ul Islam
dc.contributor.otherYönetim Bilimleri Fakültesi, İktisat Bölümü
dc.contributor.otherYönetim Bilimleri Fakültesi, İktisat Bölümü
dc.date.accessioned2023-04-28T08:56:06Z
dc.date.available2023-04-28T08:56:06Z
dc.date.issued2023
dc.departmentİHÜ, Yönetim Bilimleri Fakültesi, İktisat Bölümü
dc.description.abstractThe distance between two vertices of a simple connected graph G, denoted as (Formula presented.), is the length of the shortest path from u to v and is always symmetrical. An ordered subset (Formula presented.) of (Formula presented.) is a resolving set for G, if for ? (Formula presented.), there exists (Formula presented.) ? (Formula presented.). A resolving set with minimal cardinality is called the metric basis. The metric dimension of G is the cardinality of metric basis of G and is denoted as (Formula presented.). For the graph (Formula presented.) and (Formula presented.), their join is denoted by (Formula presented.). The vertex set of (Formula presented.) is (Formula presented.) and the edge set is (Formula presented.). In this article, we show that the metric dimension of the join of two path graphs is unbounded because of its dependence on the size of the paths. We also provide a general formula to determine this metric dimension. We also develop algorithms to obtain metric dimensions and a metric basis for the join of path graphs, with respect to its symmetries.
dc.identifier.citationZhang, C., Haidar, G., Khan, M. I., Yousafzai, F., Hila, K. ve Khan, A. I. (2023). Constant time calculation of the metric dimension of the join of path graphs. Symmetry, 15(3), 1-14. http://doi.org/10.3390/sym15030708
dc.identifier.endpage14
dc.identifier.issn2073-8994
dc.identifier.issue3
dc.identifier.scopus2-s2.0-85152703857
dc.identifier.scopusqualityQ1
dc.identifier.startpage1
dc.identifier.urihttp://doi.org/10.3390/sym15030708
dc.identifier.urihttps://hdl.handle.net/20.500.12154/2248
dc.identifier.volume15
dc.identifier.wosWOS:000961476400001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorKhan, Asad ul Islam
dc.institutionauthorid0000-0002-5131-577X
dc.language.isoen
dc.publisherMDPI
dc.relation.ispartofSymmetry
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectMetric Dimensions
dc.subjectMetric Basis
dc.subjectPath Graphs
dc.subjectJoin of Graphs
dc.titleConstant time calculation of the metric dimension of the join of path graphs
dc.typeArticle
dspace.entity.typePublication
relation.isAuthorOfPublication5d56d061-267c-4b33-8b78-b50e651ee5aa
relation.isAuthorOfPublication.latestForDiscovery5d56d061-267c-4b33-8b78-b50e651ee5aa
relation.isOrgUnitOfPublication9d1809d1-3541-41aa-94ed-639736b7e16f
relation.isOrgUnitOfPublication.latestForDiscovery9d1809d1-3541-41aa-94ed-639736b7e16f

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