Proof of a conjecture concerning the direct product of bipartite graphs

  • Authors:

  • Richard H. Hammack

  • Affiliations:

  • Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2009

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Abstract

We prove that if the direct product of two connected bipartite graphs has isomorphic components, then one of the factors admits an automorphism that interchanges its partite sets. This proves a conjecture made by Jha, Klavzar and Zmazek in 1997 [P. Jha, S. Klavzar, B. Zmazek, Isomorphic components of Kronecker product of bipartite graphs, Discussiones Mathematicae Graph Theory 17 (1997) 302-308].