ON THE METRIC DIMENSION OF A CLASS OF PLANAR GRAPHS

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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Veröffentlicht in:TWMS journal of applied and engineering mathematics 2023-01, Vol.13 (4), p.1298
Hauptverfasser: Sharma, S.K, Bhat, V.K
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Fuzzy sets
Graph theory
Graphs
Mathematical research
Mathematics
Set theory
Vertex sets
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Zusammenfassung: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.
ISSN:2146-1147
2146-1147