Almost self-inverse graphs. Issue 10 (3rd October 2019)

• Record Type: Journal Article
• Authors: Bapat, R. B.; Panda, S. K.
• Is Part Of: Linear & multilinear algebra. Volume 67:Issue 10(2019)
• Page Start: 2065
• Page End: 2076
• Publication Date: 2019-10-03
• Subjects: Almost self-inverse graph -- self-inverse graph -- boxminus corona -- corona -- even type edge -- inverse graph -- minimal path -- odd type edge -- unique perfect matching; 05C50 -- 15A09; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1481357
• Languages: English
• ISSNs: 0308-1087

Abstract

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.