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math.NT2015★ 3 cited
Ramanujan Cayley graphs of Frobenius groups
Miki Hirano, Kohei Katata, Yoshinori Yamasaki
In this paper, we determine the bound of the valency of Cayley graphs of Frobenius groups with respect to normal Cayley subsets which guarantees to be Ramanujan. We see that if the…
math.NT2013★ 4 cited
Ramanujan circulant graphs and the conjecture of Hardy-Littlewood and Bateman-Horn
Miki Hirano, Kohei Katata, Yoshinori Yamasaki
In this paper, we determine the bound of the valency of the odd circulant graph which guarantees to be a Ramanujan graph for each fixed number of vertices. In almost of the cases,…