The strong metric dimension of generalized Sierpínski graphs with pendant vertices

Abstract

Let G be a connected graph of order n having ϵ(G) end-vertices. Given a positive integer t, we denote by S(G; t) the t-Th generalized Sierpínski graph of G. In this note we show that if every internal vertex of G is a cut vertex, then the strong metric dimension of S(G; t) is given by dims(S(G; t)) = ϵ(G) (nt - 2nt-1 + 1) - n + 1/ n - 1.