On distances in generalized Sierpinski graphs

Alejandro Estrada-Moreno, Erick D. Rodriguez-Bazan, Juan A. Rodriguez-Velazquez

Published 2016-08-02Version 1

In this paper we propose formulas for the distance between vertices of a generalized Sierpi\'{n}ski graph $S(G,t)$ in terms of the distance between vertices of the base graph $G$. In particular, we deduce a recursive formula for the distance between an arbitrary vertex and an extreme vertex of $S(G,t)$, and we obtain a recursive formula for the distance between two arbitrary vertices of $S(G,t)$ when the base graph is triangle-free. From these recursive formulas, we provide algorithms to compute the distance between vertices of $S(G,t)$. In addition, we give an explicit formula for the diameter and radius of $S(G,t)$ when the base graph is a tree.