Total Perfect Codes in Tensor Products of Graphs

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.

• Type: Journal
• Year: 2008
• Where: ARSCOM
• Authors: Ghidewon Abay-Asmerom, Richard Hammack, Dewey T. Taylor
• Keywords: ARSCOM 2007, ARSCOM 2008, Tensor Product, Total Perfect Code