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arXiv · 1209.5126

Integral Cayley multigraphs over Abelian and Hamiltonian groups

Matt DeVos·Roi Krakovski·Bojan Mohar·Azhvan Sheikh Ahmady
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Abstract

It is shown that a Cayley multigraph over a group $G$ with generating multiset $S$ is integral (i.e., all of its eigenvalues are integers) if $S$ lies in the integral cone over the boolean algebra generated by the normal subgroups of $G$. The converse holds in the case when $G$ is abelian. This in particular gives an alternative, character theoretic proof of a theorem of Bridges and Mena (1982). We extend this result to provide a necessary and sufficient condition for a Cayley multigraph over a Hamiltonian group to be integral, in terms of character sums and the structure of the generating set.

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Matt DeVos, Roi Krakovski, Bojan Mohar, Azhvan Sheikh Ahmady. 2012-09-23. Integral Cayley multigraphs over Abelian and Hamiltonian groups. https://arxiv.org/abs/1209.5126

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