Cyclic Haar graphs

Authors:
Milan Hladnik;Dragan Marusic;Tomaz Pisanski
Affiliations:
IMFM, Oddelek za matematiko, Univerza v Ljubljani, Jadranska 19, 1000 Ljubljana, Slovenia;IMFM, Oddelek za matematiko, Univerza v Ljubljani, Jadranska 19, 1000 Ljubljana, Slovenia;IMFM, Oddelek za teoreticno racunalnistvo, Univerza v Ljubljani, Jadranska 19, 1000 Ljubljana, Slovenia
Venue:
Discrete Mathematics - Algebraic and topological methods in graph theory
Year:
2002

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Abstract

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