Unicyclic graphs with bicyclic inverses
Czechoslovak Mathematical Journal
A graph is nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G is a graph whose adjacency matrix is similar to A(G)−1 via a particular type of similarity. Let H denote the class of connected bipartite graphs with unique perfect matchings. Tifenbach and Kirkland (2009) characterized the unicyclic graphs in H which possess unicyclic inverses. We present a characterization of unicyclic graphs in H which possess bicyclic inverses.
Panda, Swarup Kumar, "Unicyclic graphs with bicyclic inverses" (2017). Journal Articles. 2323.