Large Cayley graphs and vertex-transitive non-Cayley graphs of given degree and diameter
نویسندگان
چکیده
For any d ≥ 5 and k ≥ 3 we construct a family of Cayley graphs of degree d, diameter k, and order at least k((d−3)/3)k. By comparison with other available results in this area we show that, for all sufficiently large d and k, our family gives the current largest known Cayley graphs of degree d and diameter k.
منابع مشابه
On the eigenvalues of normal edge-transitive Cayley graphs
A graph $Gamma$ is said to be vertex-transitive or edge- transitive if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$, respectively. Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$. Then, $Gamma$ is said to be normal edge-transitive, if $N_{Aut(Gamma)}(G)$ acts transitively on edges. In this paper, the eigenvalues of normal edge-tra...
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عنوان ژورنال:
- Journal of Graph Theory
دوره 64 شماره
صفحات -
تاریخ انتشار 2010