Geodesic
Integral Cayley multigraphs over abelian and Hamiltonian groups
Matt DeVos1 ; Roi Krakovski1 ; Bojan Mohar1 ; Azhvan Sheikh Ahmady1
1Simon Fraser University
The electronic journal of combinatorics, Tome 20 (2013) no. 2
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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.
DOI : 10.37236/2742
Classification : 05C25, 05C50
Mots-clés : Cayley graph, integral eigenvalue, abelian group, Hamiltonian group

Matt DeVos  1   ; Roi Krakovski  1   ; Bojan Mohar  1   ; Azhvan Sheikh Ahmady  1

1 Simon Fraser University 
@article{10_37236_2742,
     author = {Matt DeVos and Roi Krakovski and Bojan Mohar and Azhvan Sheikh Ahmady},
     title = {Integral {Cayley} multigraphs over abelian and {Hamiltonian} groups},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {2},
     doi = {10.37236/2742},
     zbl = {1298.05158},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2742/}
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Matt DeVos; Roi Krakovski; Bojan Mohar; Azhvan Sheikh Ahmady. Integral Cayley multigraphs over abelian and Hamiltonian groups. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/2742

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