On distances in generalized Sierpinski graphs

TL;DR

This paper develops formulas and algorithms to compute distances, diameter, and radius in generalized Sierpinski graphs based on the properties of the base graph, especially when it is triangle-free or a tree.

Contribution

It introduces recursive formulas for distances in generalized Sierpinski graphs and provides algorithms for their computation, extending understanding of their metric properties.

Findings

Recursive formulas for distances in S(G,t)

Algorithms for distance computation

Explicit formulas for diameter and radius when base graph is a tree

Abstract

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.