Degree sequence of the generalized Sierpinski graph

Abstract

The degree sequence of (ordinary) Sierpiński graphs and Hanoi graphs are determined in the literature. Also, In [ J.A. Rodriguez-Velázquez, E.D. Rodriguez-Bazan, A. Estrada-Moreno, On generalized Sierpiński graphs, Discuss. Math. Graph T., 37 (3), 2017, 547-560.] the authors determine the number of leaves (vertices of degree one) of the generalized Sierpiński S(T, t) of any tree T in terms of t, |V (T )| and the number of leaves of the base graph T . In this paper, among some other results, we generalize these results. More precisely, for every simple graph G of order n, we completely determine the degree sequence of the generalized Sierpiński graph S(G, t) of G in terms of n, t and the degree sequence of G. Also, we determine the exact value of the general first Zagreb index of S(G, t) in terms of the same parameters of G.