Girth-regular and edge-girth-regular graphsZavrtanik Drglin, Ajda (Avtor) Jajcay, Robert (Mentor) Potočnik, Primož (Komentor) graphgirthgirth-regularedge-girth-regularIn this work we discuss girth-regular and edge-girth-regular graphs. The signature of a vertex u in a graph is a k-tuple of integers, ordered from the smallest to the largest, where each integer represents the number of girth cycles that contain an edge, incident with u. We say that a graph is girth-regular, if every vertex has the same signature. If every edge is contained in the same number of girth cycles, the graph is edge-girth-regular. We present the known results about girth-regular and edge-girth-regular graphs, classify cubic graphs of both types up to girth 5, look at tetravalent edge-girth-regular graphs and present some constructions of infinite families of such graphs. We then present some new results on tetravalent edge-girth-regular graphs and the classification of tetravalent edge-girth-regular Cayley graphs of Abelian groups.20192019-10-03 07:45:22Magistrsko delo/naloga111548sl