Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 3p2 is given
We classify tetravalent -half-arc-transitive graphs of order , where and , are distinct odd primes. This result involves a subclass of tetravalent half-arc-transitive graphs of cube-free order.
A digraph is associated with a finite group by utilizing the power map defined by for all , where is a fixed natural number. It is denoted by . In this paper, the generalized quaternion and -groups are studied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a -group are determined for a -group to be a generalized quaternion group. Further, the classification of two generated -groups as abelian or non-abelian...
In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter ) by replacing the entries equal to one by more general non-vanishing complex random variables. For these ensembles, in contrast with more classical models as the Gaussian Unitary Ensemble, or the Circular Unitary Ensemble, the eigenvalues can be very explicitly computed by using the cycle structure of the permutations....