METRIC DIMENSION OF LINE GRAPH OF THE SUBDIVISION OF THE GRAPHS OF CONVEX POLYTOPES - Sharma, S. K; Bhat, V. K (TWMS journal of applied and engineering mathematics, 2023)
The metric generator for the simple connected graph [GAMMA] is the set of vertices D [[subset].bar] V([GAMMA]) with the property that every pair of vertices u, v(u [not equal to] v) [member of] V are determined (or resolved) by some vertex of D. The minimum possible cardinality of this metric generator is called the metric dimension of [GAMMA], denoted by dim([GAMMA])or [beta]([GAMMA]). 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 [D.sub.n] (exists in the literature). Keywords: Subdivision graph, resolving set, line graph, metric dimension. AMS Subject Classification: 05C12, 05C76.