Shortest paths in Sierpiński graphs

  • Authors:
  • Bing Xue;Liancui Zuo;Guanghui Wang;Guojun Li

  • Affiliations:
  • -;-;-;-

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2014

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Abstract

In [23], Klavzar and Milutinovic (1997) proved that there exist at most two different shortest paths between any two vertices in Sierpinski graphs S"k^n, and showed that the number of shortest paths between any fixed pair of vertices of S"k^n can be computed in O(n). An almost-extreme vertex of S"k^n, which was introduced in Klavzar and Zemljic (2013) [27], is a vertex that is either adjacent to an extreme vertex or incident to an edge between two subgraphs of S"k^n isomorphic to S"k^n^-^1. In this paper, we completely determine the set S"u={v@?V(S"k^n):there exist two shortest u,v-paths in S"k^n}, where u is any almost-extreme vertex of S"k^n.