Primitivity and Independent Sets in Direct Products of Vertex-Transitive Graphs

الأصل · EN

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.