Geodesic
A classification of Ramanujan unitary Cayley graphs
The electronic journal of combinatorics, Tome 17 (2010)
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The unitary Cayley graph on $n$ vertices, $X_n$, has vertex set ${\Bbb Z}/{n\Bbb Z}$, 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. ${\rm gcd}(a-b,n) = 1$. A $k$-regular graph $X$ is Ramanujan if and only if $\lambda(X) \leq 2\sqrt{k-1}$ where $\lambda(X)$ 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 $X_n$ is a Ramanujan graph.
DOI : 10.37236/478
Classification : 05C75 
@article{10_37236_478,
     author = {Andrew Droll},
     title = {A classification of {Ramanujan} unitary {Cayley} graphs},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/478},
     zbl = {1189.05147},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/478/}
}
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Andrew Droll. A classification of Ramanujan unitary Cayley graphs. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/478

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