TITLE:
Edge-Transitive Cyclic Covers of Complete Graphs with Prime Power Order
AUTHORS:
Zhaohong Huang, Yin Liu
KEYWORDS:
Cover, Complete Graph, Normal Quotient Graph, Automorphism
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.2,
February
14,
2022
ABSTRACT: Characterizing regular covers of symmetric graphs is one of the fundamental topics in the field of algebraic graph theory, and is often a key step for approaching general symmetric graphs. Complete graphs, which are typical symmetric graphs, naturally appear in the study of many symmetric graphs as normal quotient graphs. In this paper, a characterization of edge-transitive cyclic covers of complete graphs with prime power order is given by using the techniques of finite group theory and the related properties of coset graphs. Certain previous results are generalized and some new families of examples are founded.