Article ID Journal Published Year Pages File Type
8903850 Journal of Combinatorial Theory, Series B 2018 29 Pages PDF
Abstract
In order to complete (and generalize) results of Gardiner and Praeger on 4-valent symmetric graphs [3] we apply the method of lifting automorphisms in the context of elementary-abelian covering projections. In particular, the vertex- and edge-transitive graphs whose quotient by a normal p-elementary abelian group of automorphisms, for p an odd prime, is a cycle, are described in terms of cyclic and negacyclic codes. Specifically, the symmetry properties of such graphs are derived from certain properties of the generating polynomials of cyclic and negacyclic codes, that is, from divisors of xn±1∈Zp[x]. As an application, a short and unified description of resolved and unresolved cases of Gardiner and Praeger are given.
Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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