We investigate the eigenvalue spacing distributions for randomly generated 4-regular Cayley graphs on SL2(Fp) by numerically calculating their spectra. We present strong evidence that the distributions are Poisson and hence do not follow the Gaussian orthogonal ensemble. Among the Cayley graphs of SL2(Fp) we consider are the new expander graphs recently discovered by Y. Shalom. In addition, we ...

We consider the class of the topologically locally nite (in short TLF) planar vertex-transitive graphs, a class containing in particular all the one-ended planar Cayley graphs and the normal transitive tilings. We characterize these graphs with a nite local representation and a special kind of nite state automaton named labeling scheme. As a result, we are able to enumerate and describe all TLF...

We investigate the eigenvalue spacing distributions for randomly generated 4-regular Cayley graphs on SL2(Fp) by numerically calculating their spectra. We present strong evidence that the distributions are Poisson and hence do not follow the Gaussian orthogonal ensemble. Among the Cayley graphs of SL2(Fp) we consider are the new expander graphs recently discovered by Y. Shalom. In addition, we ...

The Platonic graphs πn arise in several contexts, most simply as a quotient of certain Cayley graphs associated to the projective special linear groups. We show that when n = p is prime, πn can be viewed as a complete multigraph in which each vertex is itself a wheel on n + 1 vertices. We prove a similar structure theorem for the case of an arbitrary prime power. These theorems are then used to...

Static DHT topologies influence important features of such DHTs such as scalability, communication load balancing, routing efficiency and fault tolerance. Nevertheless, it is commonly recognized that the primary difficulty in designing DHT is not in static DHT topologies, but in the dynamic DHT algorithm which adapts various static DHT topologies to a dynamic network at Internet. As a direct co...

‎darafsheh and assari in [normal edge-transitive cayley graphs on non-abelian groups of order 4p‎, ‎where $p$ is a prime number‎, ‎sci‎. ‎china math‎., ‎56 (1) (2013) 213-219.] classified the connected normal edge transitive and‎ ‎$frac{1}{2}-$arc-transitive cayley graph of groups of order $4p$‎. ‎in this paper we continue this work by classifying the‎ ‎connected cayley graph of groups of order...