Abstract

It is easily shown that two finite graphs share a common (possibly infinite) cover if and only if they have the same degree refinement. Angluin and Gardiner ( J. Combin. Theory Ser. B 30 (1981), 184–187) show that any pair of regular graphs with identical valence share a common finite cover. More generally, they conjecture that any pair of graphs with the same degree refinement share a common finite cover. In this paper, their conjecture is verified and a method of constructing a finite common covering of any pair of graphs with the same degree refinement is defined.

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