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
Subjects
Fuzzy sets
Graph theory
Mathematical research
Set theory
India
Online AccessGet full text
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