METRIC DIMENSION OF LINE GRAPH OF THE SUBDIVISION OF THE GRAPHS OF CONVEX POLYTOPES

The metric generator for the simple connected graph [GAMMA] is the set of vertices D [[subset].bar] V([GAMMA]) with the property that every pair of vertices u, v(u [not equal to] v) [member of] V are determined (or resolved) by some vertex of D. The minimum possible cardinality of this metric genera...

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Published inTWMS journal of applied and engineering mathematics Vol. 13; no. 2; p. 448
Main Authors Sharma, S. K, Bhat, V. K
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.04.2023
Elman Hasanoglu
Subjects
Apexes
Convex surfaces
Graph theory
Mathematical research
Mathematics
Polytopes
India
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ISSN2146-1147
2146-1147

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Summary:The metric generator for the simple connected graph [GAMMA] is the set of vertices D [[subset].bar] V([GAMMA]) with the property that every pair of vertices u, v(u [not equal to] v) [member of] V are determined (or resolved) by some vertex of D. The minimum possible cardinality of this metric generator is called the metric dimension of [GAMMA], denoted by dim([GAMMA])or [beta]([GAMMA]). In this article, we determine the exact metric dimension and some other properties of the line graph of the subdivision graph of the graph of convex polytope [D.sub.n] (exists in the literature). Keywords: Subdivision graph, resolving set, line graph, metric dimension. AMS Subject Classification: 05C12, 05C76.
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ISSN:2146-1147
2146-1147