In this paper, a complete classification is given of all the regular metacyclic covers of the Petersen graph, whose fibre-preserving groups act edge-transitively. Moreover, as an application, it is proved that there is no cubic 1-arc-regular graph with order 5m where m is a cube-free integer and coprime to 15.
['Jiangmin Pan', 'Zhaohong Huang']
Edge-Transitive Regular Metacyclic Covers of the Petersen Graph