Geodesic
Edge-transitive products
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 4, pp. 837-850.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 edge-transitive 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 non-trivial 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, edge- and 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.
Classification : 05C76, 05C25
Keywords: edge-transitive graphs, vertex-transitive graphs, graph products 
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     title = {Edge-transitive products},
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Hammack, Richard; Imrich, Wilfried; Klavžar, Sandi. Edge-transitive products. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 4, pp. 837-850. http://geodesic.mathdoc.fr/item/JAC_2016__43_4_a3/