Semisymmetric Zp-covers of the C20 graph

A graph X is said to be G-semisymmetric if it is regular and there exists a subgroup G of A:=Aut(X) acting transitively on its edge set but not on its vertex set. In the case of G=A, we call X a semisymmetric graph. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields. In this study, by applying concept linear algebra, we classify the connected semisymmetric zp-covers of the C20 graph.

On Pentavalent Arc-Transitive Graphs

In this paper, a characterization of all pentavalent arc-transitive graphs is given. It is shown that each pentavalent arc-transitive covering graph Γ is a regular simple or elementary abelian covering graph. In particular, the elementary abelian covering groups are ℤ3, ℤ5 or a subgroup of [Formula: see text].

On 3-arc-transitive covers of the dodecahedron graph

In this paper, the following problem is considered: does there exist a t-arc-transitive regular covering graph of an s-arc-transitive graph for positive integers t greater than s? In order to answer this question, we classify all arc-transitive cyclic regular covers of the dodecahedron graph. Two infinite families of 3-arc-transitive abelian covering graphs are given, which give more specific examples that for an s-arc-transitive graph there exist (s+1)-arc-transitive covering graphs.