On distances in Sierpiński graphs: Almost-extreme vertices and metric dimension
Sandi Klavžar, Sara Sabrina Zemljič · Applicable Analysis and Discrete Mathematics · 2013
Sierpi?ski graphs Sn 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 Sn p is introduced as a vertex that is either adjacent to an extreme vertex of Sn p or is incident to an edge between two subgraphs of Sn p isomorphic to Snp-1. Explicit formulas are given for the distance in Sn 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 Sierpi?ski graphs.