On some graphs which possess inverses.

A graphis nonsingular if its adjacency matrixis nonsingular. A nonsingular graphis said to have an inverseifis signature similar to a nonnegative matrix. An-graphis a bipartite graph with a unique perfect matching. We introduce the ‘even’ness of a nonmatching edge and show that under certain conditions a connected-graph has an inverse if and only ifis bipartite, whereis the set of all even nonmatching edges. This extends some known results, providing us with a larger class of graphs possessing inverses. [ABSTRACT FROM PUBLISHER]