Cyclic Haar graphs

For a given group <f>Γ</f> with a generating set <f>A</f>, a dipole with <f>|A|</f> parallel arcs (directed edges) labeled by elements of <f>A</f> gives rise to a voltage graph whose covering graph, denoted by <f>H(Γ,A)</f> is a bipartite, regular graph, called a bi-Cayley graph. In the case when <f>Γ</f> is abelian we refer to <f>H(Γ,A)</f> as the Haar graph of <f>Γ</f> with respect to the symbol <f>A</f>. In particular for <f>Γ</f> cyclic the above graph is referred to as a cyclic Haar graph. A basic theory of cyclic Haar graphs is presented. [Copyright &y& Elsevier]