Abstract
The class of non-bipartite unicyclic graphs with a unique perfect matching, denoted by , is considered in this article. This article describes the entries of the inverse of the adjacency matrix of a graph in . It is proved that the inverse graph of a graph in is always non-bipartite. In this article, we characterize the graphs in whose inverses are mixed graphs. Among all such graphs in we identify those graphs whose inverses are quasi-bipartite. Furthermore, characterizations of unicyclic graphs in possessing unicyclic and bicyclic inverses are also provided in this article.
Acknowledgements
The authors sincerely thank the referees and editors for carefully reading the manuscript and their suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).