This article is cited in 2 papers

RESEARCH ARTICLE

Semisymmetric $Z_{p}$-covers of the $C20$ graph

A. A. Talebi, N. Mehdipoor

Faculty of Mathematics, University of Mazandaran, Iran

Abstract: A graph $ X$ is said to be $G$-semisymmetric if it is regular and there exists a subgroup $G$ of $A := \operatorname{Aut}(X)$ 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 $z_{p}$-covers of the $C20$ graph.

Keywords: invariant subspaces, homology group, $C20$ graph, semisymmetric graphs, regular covering, lifting automorphisms.

MSC: 05C25, 20B25

Received: 12.07.2016

Language: English

DOI: 10.12958/adm252