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3-Circulant Graphs

George J. Davis1, Gayla S. Domke1
1Department of Mathematics and Statistics Georgia State University, Atlanta, GA 30303

Abstract

A 3-regular graph G is called a 3-circulant if its adjacency matrix A(G) is a circulant matrix. We show how all disconnected 3-circulants are made up of connected 3-circulants and classify all connected 3-circulants as one of two basic types. The rank of A(G) is then completely determined for all 3-circulant graphs G.