Isomorphic tetravalent cyclic Haar graphs

Abstract

Let $S$ be a subset of the cyclic group ${\mathbb{Z}}_n$. The cyclic Haar graph $H({\mathbb{Z}}_n,S)$ is the bipartite graph with color classes ${\mathbb{Z}}_n^{+}$ and ${\mathbb{Z}}_n^{-},$ and edges $\{x^{+},y^{-}\},$ where $x,y\in {\mathbb{Z}}_n$ and $y-x\in S$. In this paper we give sufficient and necessary conditions for the isomorphism of two connected cyclic Haar graphs of valency 4.

References in corpus (1)

• Equivalence of sparse circulants: the bipartite Ádám problem

Cited by in corpus (1)

• The number of cyclic configurations of type $(v_3)$ and the isomorphism problem