Vertex-Transitive Direct Products of Graphs
It is known that for graphs $A$ and $B$ with odd cycles, the direct product $A\times B$ is vertex-transitive if and only if both $A$ and $B$ are vertex-transitive. But this is not necessarily true if one of $A$ or $B$ is bipartite, and until now there has been no characterization of such vertex-transitive direct products. We prove that if $A$ and $B$ are both bipartite, or both non-bipartite, then $A\times B$ is vertex-transitive if and only if both $A$ and $B$ are vertex-transitive. Also, if $A$ has an odd cycle and $B$ is bipartite, then $A\times B$ is vertex-transitive if and only if both $A\times K_2$ and $B$ are vertex-transitive.
1987 ◽
Vol 42
(2)
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pp. 147-172
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2001 ◽
Vol 44
(2)
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pp. 379-388
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2008 ◽
Vol Vol. 10 no. 3
(Graph and Algorithms)
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1966 ◽
Vol 18
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pp. 1004-1014
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1983 ◽
Vol 26
(2)
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pp. 233-240
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1960 ◽
Vol 12
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pp. 447-462
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2009 ◽
Vol 49
(3)
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pp. 619-630
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