METRIC DIMENSION OF LINE GRAPH OF THE SUBDIVISION OF THE GRAPHS OF CONVEX POLYTOPES

METRIC DIMENSION OF LINE GRAPH OF THE SUBDIVISION OF THE GRAPHS OF CONVEX POLYTOPES

S. K. Sharma, V. K. Bhat

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Abstract

The metric generator for the simple connected graph is the set of vertices Y   V() with the property that every pair of vertices u; v(u 6= v) 2 V are determined (or resolved) by some vertex of Y. The minimum possible cardinality of this metric generator is called the metric dimension of, denoted by dim()or  (). In this article, we determine the exact metric dimension and some other properties of the line graph of the subdivision graph of the graph of convex polytope Dn (exists in the literature).

Keywords

Subdivision graph, resolving set, line graph, metric dimension.