On Distances in Sierpiński Graphs: Almost-extreme Vertices and Metric Dimension
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چکیده
Sierpiński graphs S p form an extensively studied family of graphs of fractal nature applicable in topology, mathematics of the Tower of Hanoi, computer science, and elsewhere. An almost-extreme vertex of S p is introduced as a vertex that is either adjacent to an extreme vertex of S p or is incident to an edge between two subgraphs of S p isomorphic to S n−1 p . Explicit formulas are given for the distance in S p between an arbitrary vertex and an almostextreme vertex. The formulas are applied to compute the total distance of almost-extreme vertices and to obtain the metric dimension of Sierpiński graphs.
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تاریخ انتشار 2012