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Spectra of Heisenberg graphs over finite rings

Pages: 213 - 222, Issue Special, July 2003

 Abstract        Full Text (252.2K)              

M. DeDeo - Math. Dept., U.C.S.D., La Jolla, CA 92092-0112, United States (email)
M. Martínez - Math. Dept., U.C.S.D., La Jolla, CA 92092-0112, United States (email)
A. Medrano - Math. Dept., U.C.S.D., La Jolla, CA 92092-0112, United States (email)
M. Minei - Math. Dept., U.C.S.D., La Jolla, CA 92092-0112, United States (email)
H. Stark - Math. Dept., U.C.S.D., La Jolla, CA 92092-0112, United States (email)
A. Terras - Math. Dept., U.C.S.D., La Jolla, CA 92092-0112, United States (email)

Abstract: 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:  Cayley graph, spectrum adjacency matrix
Mathematics Subject Classification:  Primary: 11T99; Secondary: 20C33, 05C50.

Received: September 2002; Published: April 2003.