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Edge-Transitive Lexicographic and Cartesian Products

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Imrich W., Iranmanesh A., Klavžar S., Soltani A.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 4

857-865

In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G ◦ H of a connected graph G that is not complete by a graph H, we show that it is edge-transitive if and only if G is edge-transitive and H is edgeless. If the first factor of G ∘ H is non-trivial and complete, then G ∘ H is edge-transitive if and only if H is the lexicographic product of a complete graph by an edgeless graph. This fixes an error of Li, Wang, Xu, and Zhao [11]. For the Cartesian product it is shown that every connected Cartesian product of at least two non-trivial factors is edge-transitive if and only if it is the Cartesian power of a connected, edge- and vertex-transitive graph.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Imrich W.

1 Iranmanesh A.

1 Klavžar S.

1 Soltani A.

1 2016

Wyniki wyszukiwania

Edge-Transitive Lexicographic and Cartesian Products