Primitivity and independent sets in direct products of vertex-transitive graphs

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Abstract

We introduce the concept of the primitivity of independent set in vertex-transitive graphs, and investigate the relationship between the primitivity and the structure of maximum independent sets in direct products of vertex-transitive graphs. As a consequence of our main results, we positively solve an open problem related to the structure of independent sets in powers of vertex-transitive graphs. © 2010 Wiley Periodicals, Inc. J Graph Theory 67: 218-225, 2011

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