Almost self-inverse graphs. Issue 10 (3rd October 2019) - Bapat, R. B.; Panda, S. K.
ABSTRACT: Let G be a simple graph with adjacency matrix A ( G ) . The inverse of the graph G, when it exists, is the unique weighted graph whose adjacency matrix is similar to A ( G ) − 1 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.