SOME PLANAR GRAPHS WITH TEN-SIDED FACES AND THEIR METRIC DIMENSION

Let [GAMMA] = (V, E) be a non-trivial planar connected graph with vertex set V and edge set E. A set of ordered vertices R from V ([GAMMA]) is said to be a resolving set for [GAMMA] if each vertex of [GAMMA] is uniquely determined by its vector of distances to the vertices of R. The number of vertic...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 14; no. 2; p. 834
Main Authors Sharma, S.K, Bhat, V.K
Format Journal Article
LanguageEnglish
Published Turkic World Mathematical Society 01.04.2024
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ISSN2146-1147

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Summary:Let [GAMMA] = (V, E) be a non-trivial planar connected graph with vertex set V and edge set E. A set of ordered vertices R from V ([GAMMA]) is said to be a resolving set for [GAMMA] if each vertex of [GAMMA] is uniquely determined by its vector of distances to the vertices of R. The number of vertices in a smallest resolving set is called the metric dimension of [GAMMA]. In this article, we study the metric dimension for two families of planar graphs, each of which is shown to have an independent minimum resolving set with cardinality three. Keywords: Metric dimension, independent set, metric basis, planar graph, resolving set, connected graph. AMS Subject Classification: 05C10, 05C12, 05C90.
ISSN:2146-1147