The unitary Cayley graph on n vertices, Xn, has vertex set Z/nZ, and two vertices a and b are connected by an edge if and only if they differ by a multiplicative unit modulo n, i.e. gcd(a - b, n) = 1. A k-regular graph X is Ramanujan if and only i (X) ≤ 2√k - 1 where (X) is the second largest absolute value of the eigenvalues of the adjacency matrix of X. We obtain a complete characterization of the cases in which the unitary Cayley graph Xn is a Ramanujan graph.
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CITATION STYLE
Droll, A. (2010). A classification of Ramanujan unitary cayley graphs. Electronic Journal of Combinatorics, 17(1), 1–6. https://doi.org/10.37236/478