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.
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