On distances in generalized Sierpinski graphs

Identifier:  imarina:5133138

Handle: https://hdl.handle.net/20.500.11797/imarina5133138

Authors:  Estrada-Moreno, Alejandro; Rodriguez-Bazan, Erick D; Rodriguez-Velazquez, Juan A

Abstract:
In this paper we propose formulas for the distance between vertices of a generalized Sierpi nski 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.