Multiple Kronecker covering graphs

Authors:
Wilfried Imrich;Toma Pisanski
Affiliations:
Montanuniversität Leoben, Austria;IMFM, University of Ljubljana, Slovenia and University of Primorska, Slovenia
Venue:
European Journal of Combinatorics
Year:
2008

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Abstract

A graph may be the Kronecker cover in more than one way. In this note we explore this phenomenon and apply it to show that the minimal common cover of two graphs need not be unique. We provide examples of graphs of the same size with non-unique common double covers and of isovalent graphs of the same size with non-unique minimal regular common covers.