1. EDGE-TRANSITIVE LEXICOGRAPHIC AND CARTESIAN PRODUCTS.
- Author
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IMRICH, WILFRIED, IRANMANESH, ALI, KLAVŽAR, SANDI, and SOLTANI, ABOLGHASEM
- Subjects
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ANALYTIC geometry , *GRAPH connectivity , *COMPLETE graphs , *MATHEMATICAL analysis , *ERROR analysis in mathematics - Abstract
In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G o 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 o H is non-trivial and complete, then G o 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. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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