Edge-transitive products
نویسندگان
چکیده
This paper concerns finite, edge-transitive direct and strong products, as well as infinite weak Cartesian products. We prove that the direct product of two connected, non-bipartite graphs is edge-transitive if and only if both factors are edgetransitive and at least one is arc-transitive, or one factor is edge-transitive and the other is a complete graph with loops at each vertex. Also, a strong product is edge-transitive if and only if all factors are complete graphs. In addition, a connected, infinite nontrivial Cartesian product graph G is edge-transitive if and only if it is vertex-transitive and if G is a finite weak Cartesian power of a connected, edgeand vertex-transitive graph H , or if G is the weak Cartesian power of a connected, bipartite, edge-transitive graph H that is not vertex-transitive.
منابع مشابه
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