Ranks of Line Graphs of Regular Graphs

George J. Davis1, Gayla S. Domke1, Charles R. Garner1, Jr. 1
1Department of Mathematics and Statistics Georgia State University, Atlanta, GA 30303

Abstract

We consider the rank of the adjacency matrix of the line graph for some classes of regular graphs. In particular, we study the line graphs of cycles, paths, complete graphs, complete bipartite and multipartite graphs, circulant graphs of degrees three and four, and some Cartesian graph products.