Geodesic
On automorphisms of direct products of Cayley graphs on abelian groups
Dave Witte Morris1
1University of Lethbridge
The electronic journal of combinatorics, Tome 28 (2021) no. 3
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Let $X$ and $Y$ be connected Cayley graphs on abelian groups, such that no two distinct vertices of $X$ have exactly the same neighbours, and the same is true about $Y$. We show that if the number of vertices of $X$ is relatively prime to the number of vertices of $Y$, then the direct product $X \times Y$ has only the obvious automorphisms (namely, the ones that come from automorphisms of its factors $X$ and $Y$). This was not previously known even in the special case where $Y = K_2$ has only two vertices. The proof of this special case is short and elementary. The general case follows from the special case by standard arguments.
DOI : 10.37236/9940
Classification : 05C25, 05C76
Mots-clés : canonical bipartite double cover of a graph, twin-free graph

Dave Witte Morris  1

1 University of Lethbridge 
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     author = {Dave Witte Morris},
     title = {On automorphisms of direct products of {Cayley} graphs on abelian groups},
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     doi = {10.37236/9940},
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Dave Witte Morris. On automorphisms of direct products of Cayley graphs on abelian groups. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/9940

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