The strong metric dimension of generalized Sierpiński graphs with pendant vertices

Abstract

Let G be a connected graph of order n having ɛ(G) end-vertices. Given a positive integer t, we denote by S(G, t) the t-th generalized Sierpiński 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 dim_s(S(G, t)) = (ɛ(G)(n^t − 2n^t − 1 + 1) − n + 1) / (n − 1).