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29 March 2024
 
  » arxiv » 1608.0769

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On distances in generalized Sierpinski graphs
Alejandro Estrada-Moreno ; Erick D. Rodriguez-Bazan ; Juan A. Rodriguez-Velazquez ;
Date 2 Aug 2016
AbstractIn 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.
Source arXiv, 1608.0769
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