American Institute of Mathematical Sciences

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2003, 2003(Special): 213-222. doi: 10.3934/proc.2003.2003.213

Spectra of Heisenberg graphs over finite rings

M. DeDeo 1, , M. Martínez 1, , A. Medrano 1, , M. Minei 1, , H. Stark 1, and  A. Terras 1,

1. 

Math. Dept., U.C.S.D., La Jolla, CA 92092-0112, United States, United States, United States, United States, United States, United States

Received  September 2002 Published  April 2003

We investigate spectra of Cayley graphs for the Heisenberg group over finite rings $\mathbb(Z)$/$p^n\mathbb(Z)$, where $p$ is a prime. Emphasis is on graphs of degree four. We show that for odd $p$ there is only one such connected graph up to isomorphism. When $p = 2$, there are at most two isomorphism classes. We study the spectra using representations of the Heisenberg group. This allows us to produce histograms and butterfly diagrams of the spectra.
Keywords: spectrum adjacency matrix, Cayley graph.
Mathematics Subject Classification: Primary: 11T99; Secondary: 20C33, 05C5.
Citation: M. DeDeo, M. Martínez, A. Medrano, M. Minei, H. Stark, A. Terras. Spectra of Heisenberg graphs over finite rings. Conference Publications, 2003, 2003 (Special) : 213-222. doi: 10.3934/proc.2003.2003.213
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