ON THE METRIC DIMENSION OF A CLASS OF PLANAR GRAPHS

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

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Published inTWMS journal of applied and engineering mathematics Vol. 13; no. 4; p. 1298
Main Authors Sharma, S.K, Bhat, V.K
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2023
Elman Hasanoglu
Subjects
Apexes
Fuzzy sets
Graph theory
Graphs
Mathematical research
Mathematics
Set theory
Vertex sets
India
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ISSN2146-1147
2146-1147

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Abstract Let H = (V, E) be a non-trivial connected graph with vertex set V and edge set E. A set of ordered vertices [R.sub.m] from V (H) is said to be a resolving set for H if each vertex of H is uniquely determined by its vector of distances to the vertices of [R.sub.m]. The number of vertices in a smallest resolving set is called the metric dimension of H. In this article, we study the metric dimension for a rotationally symmetric family of planar graphs, each of which is shown to have an independent minimum resolving set of cardinality three. Keywords: Resolving set, metric dimension, rotationally symmetric plane graph, independent set. AMS Subject Classification: 05C12, 05C90.
AbstractList Let H = (V;E) be a non-trivial connected graph with vertex set V and edge set E. A set of ordered vertices Rm from V (H) is said to be a resolving set for H if each vertex of H is uniquely determined by its vector of distances to the vertices of Rm. The number of vertices in a smallest resolving set is called the metric dimension of H. In this article, we study the metric dimension for a rotationally symmetric family of planar graphs, each of which is shown to have an independent minimum resolving set of cardinality three.
Let H = (V, E) be a non-trivial connected graph with vertex set V and edge set E. A set of ordered vertices [R.sub.m] from V (H) is said to be a resolving set for H if each vertex of H is uniquely determined by its vector of distances to the vertices of [R.sub.m]. The number of vertices in a smallest resolving set is called the metric dimension of H. In this article, we study the metric dimension for a rotationally symmetric family of planar graphs, each of which is shown to have an independent minimum resolving set of cardinality three.
Let H = (V, E) be a non-trivial connected graph with vertex set V and edge set E. A set of ordered vertices [R.sub.m] from V (H) is said to be a resolving set for H if each vertex of H is uniquely determined by its vector of distances to the vertices of [R.sub.m]. The number of vertices in a smallest resolving set is called the metric dimension of H. In this article, we study the metric dimension for a rotationally symmetric family of planar graphs, each of which is shown to have an independent minimum resolving set of cardinality three. Keywords: Resolving set, metric dimension, rotationally symmetric plane graph, independent set. AMS Subject Classification: 05C12, 05C90.
Audience Academic
Author Sharma, S.K
Bhat, V.K
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Elman Hasanoglu
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Snippet Let H = (V, E) be a non-trivial connected graph with vertex set V and edge set E. A set of ordered vertices [R.sub.m] from V (H) is said to be a resolving set...
Let H = (V;E) be a non-trivial connected graph with vertex set V and edge set E. A set of ordered vertices Rm from V (H) is said to be a resolving set for H if...
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SubjectTerms Apexes
Fuzzy sets
Graph theory
Graphs
Mathematical research
Mathematics
Set theory
Vertex sets
Title ON THE METRIC DIMENSION OF A CLASS OF PLANAR GRAPHS
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Volume 13
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