ON THE METRIC DIMENSION OF A CLASS OF PLANAR GRAPHS

ON THE METRIC DIMENSION OF A CLASS OF PLANAR GRAPHS

S. K. Sharma, V. K. Bhat

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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 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.

Keywords

Resolving set, metric dimension, rotationally symmetric plane graph, inde- pendent set.