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Ars Combinatoria

  • Research article

Total Perfect Codes in Tensor Products of Graphs

Ghidewon Abay-Asmerom1, Richard H.Hammack2, Dewey T.Taylor1
1Department of Mathematics and Applied Mathematics Virginia Commonwealth University Richmond, VA 23284-2014, USA
2 Department of Mathematics and Applied Mathematics Virginia Commonwealth University Richmond, VA 23284-2014, USA
  • Published: 31/07/2008

Abstract

A total perfect code in a graph is a subset of the graph’s vertices with the property that each vertex in the graph is adjacent to exactly one vertex in the subset. We prove that the tensor product of any number of simple graphs has a total perfect code if and only if each factor has a total perfect code.

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Citation
Ghidewon Abay-Asmerom, Richard H.Hammack, Dewey T.Taylor. Total Perfect Codes in Tensor Products of Graphs[J], Ars Combinatoria, Volume 088. 129-134. .