Vertex resolvability of convex polytopes with n-paths of length p
Sahil Sharma, Vijay Kumar Bhat · International Journal of Computer Mathematics Computer Systems Theory · 2022
Let G=(V,E) be a simple, connected, and undirected graph. The distance between two vertices u,v∈V, denoted by d(u,v), is the length of the shortest path connecting u and v. A subset of vertices RG is said to be a resolving set for G if for any two distinct vertices u1,u2∈ V, there exist a vertex α∈RG such that d(u1,α)≠d(u2,α). A minimal resolving set is called a metric basis, and the cardinality of the basis set is called the metric dimension of G, denoted by β(G). In this article, we find the metric dimension for two infinite families of plane graphs Υn and Πn,p, where Υn is obtained by the combination of 2n copies of bipartite graphs (K1,3), and Πn,p is obtained by the combination of double antiprism graph with antiprism graph and then adding n-paths of length p.