The strong metric dimension of generalized Sierpiński 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 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)) = ε(G) n t − 2n t−1 + 1 − n + 1 n − 1 .

Polynomials and General Degree‐Based Topological Indices of Generalized Sierpinski Networks

“…In [50], the authors discussed some energies of the Sierpinski gasket. e authors in [51] computed strong metric dimension of generalized S n k having isolated pendant nodes. Total colorings of S n k were discussed in [52].…”

On the Geodesic Identification of Vertices in Convex Plane Graphs

“…(i) e strong metric dimension problem has been solved for Sierpiński graph in [20], for hamming graphs in [21], for some convex polytopes in [22,23], for wheel related graphs (including n-fold wheel, sunflower, helm, and friendship graphs) in [24], for path, cycle, complete, complete bipartite, and tree graphs in [25], for Cayley graphs in [26], for Cartesian sum graphs in [27], for the power graph of a finite group in [28], for distance-hereditary graphs in [29], for generalized butterfly and starbarbell graphs in [30], for antiprism and king graphs in [31], for sun, windmill, and Möbius ladder graphs in [32], and for crossed prism in [33]. (ii) e strong metric dimension of various products of graphs including Cartesian product, direct product, strong product, lexicographic product, rooted product, and corona product has been supplied through the articles in [26,27,30,31,[33][34][35][36][37][38][39].…”

Recognizing generalized Sierpiński graphs

“…In recent years several publications followed this idea, and it seems that generalized Sierpiński graphs will become similarly popular as Sierpiński graphs: total colorings of generalized Sierpiński graphs were investigated in [7], the Randić index in [24], and the generalized Randić index in [5]. The strong metric dimension was treated in [3], and in [4] the chromatic number, the vertex cover number, the clique number and the domination number of generalized Sierpiński graphs. A discussion on Roman domination can be found in [23], and in [18] an investigation of generalized Sierpiński graphs with respect to connectivity and other properties, such as Hamiltonicity.…”