Group inverses of matrices associated with certain graph classes

Abstract

We obtain formulae for group inverses of matrices that are associated with a new class of digraphs obtained from stars. This new class contains both bipartite and non-bipartite graphs. Expressions for the group inverse of matrices corresponding to double star digraphs and the adjacency matrix of certain undirected multi-star graphs are also proven. A blockwise representation of the inverse or group inverse of the adjacency matrix of the Dutch windmill graph is presented.