Abstract
A graph is nonsingular if its adjacency matrix is nonsingular. A nonsingular graph is said to have an inverse if is signature similar to a nonnegative matrix. An -graph is 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 if is bipartite, where is the set of all even nonmatching edges. This extends some known results, providing us with a larger class of graphs possessing inverses.
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