ABSTRACT
Let G be a simple graph with adjacency matrix . The inverse of the graph G, when it exists, is the unique weighted graph whose adjacency matrix is similar to
via a particular type of similarity. An invertible graph G is said to be an almost self-inverse graph if the inverse graph of G can be obtained from G just by joining two nonadjacent vertices. We present a characterization of almost self-inverse graphs of a specific class of graphs which contains the class of nonsingular trees.
Acknowledgments
The authors sincerely thank the referees and the editors for their valuable suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.