Arc-transitive and edge-transitive graphs are widely used in computer networks. Therefore, it is very useful to introduce and study the properties of these graphs. A graph ! can be called G-edge-transitive (G-E-T) or G-arc-transitive (G-A-T) if G acts transitively on its edges or arc set, where G6Autð!Þ, respectively. A regular covering projection (C-P) p : ! ! ! is E-T or A-T if an E-R or A-T subgroup of Autð!Þ lifts under p: In this paper, we first study all p-elementary abelian (E-A) regular covers of Wreath graph Wð2, 3Þ and then investigate (E-T) regular Zp-covers of the Foster graph F26A
