On distances in generalized Sierpiński graphs
Copyright policy )On distances in generalized Sierpiński graphs
In this paper we propose formulas for the distance between vertices of a generalized Sierpi?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.
Distance in graphs, Graph algorithms (graph-theoretic aspects), 05C76, 05C12, generalized Sierpiński graphs, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Sierpiński graphs, distances in graphs
Distance in graphs, Graph algorithms (graph-theoretic aspects), 05C76, 05C12, generalized Sierpiński graphs, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Sierpiński graphs, distances in graphs
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