Metric properties of generalized Sierpiński graphs over stars

Abstract For a graph G , an infinite series of self-similar graphs is formed by the generalized Sierpinski graphs S G t , t ≥ 1 . In the case when G is complete we have the classical Sierpinski graphs S n t = S K n t . In this paper the Wiener index, the Wiener complexity, and the metric dimension of their antipode family S K 1 , n t are determined. Along the way some other properties of the family are also obtained such as the number of vertex and edge orbits of the automorphism group of S K 1 , n t .

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