Edge-transitive lexicographic and Cartesian products
نویسندگان
چکیده
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, edgeand vertex-transitive graph.
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ورودعنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 36 شماره
صفحات -
تاریخ انتشار 2016