dc.contributor.author Balaraman, Ganesan en_US dc.contributor.author Kumar, Sanjay Sampath en_US dc.contributor.author Sundareswaran, Raman en_US dc.date.accessioned 2021-01-22T11:43:15Z dc.date.available 2021-01-22T11:43:15Z dc.date.issued 2021 dc.identifier.citation Balaraman, G., Kumar, S. S. & Sundareswaran, R. (2021). Geodetic domination integrity in graphs. TWMS Journal of Applied and Engineering Mathematics, 11(SI), 258-267. en_US dc.identifier.issn 2146-1147 dc.identifier.issn 2587-1013 dc.identifier.uri https://hdl.handle.net/11729/3042 dc.identifier.uri http://jaem.isikun.edu.tr/web/index.php/archive/109-vol11-special-issue/655 dc.description.abstract Reciprocal version of product degree distance of cactus graphs Let G be a simple graph. A subset S ⊆ V (G) is a said to be a geodetic set if every vertex u /∈ S lies on a shortest path between two vertices from S. The minimum cardinality of such a set S is the geodetic number g(G) of G. A subset D ⊆ V (G) is a dominating set of G if every vertex u /∈ D has at least one neighbor in D. The domination number γ(G) is the minimum cardinality of a dominating set of G. A subset is said to be a geodetic dominating set of G if it is both a geodetic and a dominating set. The geodetic domination number γg(G) is the minimum cardinality among all geodetic dominating sets in G. The geodetic domination integrity of a graph G is defined by DIg(G) = min{|S| + m(G − S) : S is a geodetic dominating set of G}, where m(G − S) denotes the order of the largest component in G−S. In this paper, we study the concepts of geodetic dominating integrity of some families of graphs and derive some bounds for the geodetic domination integrity. Also we obtain geodetic domination integrity of some cartesian product of graphs. en_US dc.language.iso eng en_US dc.publisher Işık University Press en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.rights Attribution-NonCommercial-NoDerivs 3.0 United States * dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/us/ * dc.subject Geodetic sets en_US dc.subject Geodetic dominating sets en_US dc.subject Geodetic domination integrity sets en_US dc.title Geodetic domination integrity in graphs en_US dc.type article en_US dc.description.version Publisher's Version en_US dc.relation.journal TWMS Journal of Applied and Engineering Mathematics en_US dc.identifier.volume 11 dc.identifier.issue SI dc.identifier.startpage 258 dc.identifier.endpage 267 dc.peerreviewed Yes en_US dc.publicationstatus Published en_US dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Başka Kurum Yazarı en_US
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