Equiarboreal graphs

Abstract

A graphX is said to beequiarboreal if the number of spanning trees containing a specified edge inX is independent of the choice of edge. We prove that any graph which is a colour class in an association scheme (and thus any distance regular graph) is equiarboreal. We note that a connected equiarboreal graph withM edges andn vertices has edge-connectivity at leastM/(n−1).

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Godsil, C.D. Equiarboreal graphs. Combinatorica 1, 163–167 (1981). https://doi.org/10.1007/BF02579272

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AMS subject classification (1980)

  • 05 C 05, 05 B 30
  • 15 A 18, 05 C 40