International Conference on Graph Theory and Combinatorics

May 16 – 18, 2014
Rogla, Slovenia
UTC timezone

On circulant graphs that are isomorphic to Cayley graphs of more than one abelian group

Not scheduled
Rogla, Slovenia

Speaker

Prof. Ted Dobson (Mississippi State University and University of Primorska)

Description

We show that for certain integers $n$, the problem of whether or not a circulant digraph $\Gamma$ of order $n$ is also isomorphic to a Cayley digraph of some other abelian group $G$ of order $n$ reduces to the question of whether or not a natural subgroup of the full automorphism group contains more than one regular abelian group up to isomorphism (as opposed to the full automorphism group). A necessary and sufficient condition is then given for such circulants to be isomorphic to Cayley digraphs of more than one abelian group. A generalization of a permutation group theoretic result of Muzychuk is one of the main tools. This is joint work with Joy Morris.

Primary author

Prof. Ted Dobson (Mississippi State University and University of Primorska)

Presentation materials

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