Back to Search Start Over

Inverses of Bipartite Graphs.

Authors :
Yang, Yujun
Ye, Dong
Source :
Combinatorica; Oct2018, Vol. 38 Issue 5, p1251-1263, 13p
Publication Year :
2018

Abstract

Let G be a bipartite graph with adjacency matrix A. If G has a unique perfect matching, then A has an inverse A<superscript>1</superscript> which is a symmetric integral matrix, and hence the adjacency matrix of a multigraph. The inverses of bipartite graphs with unique perfect matchings have a strong connection to Möbius functions of posets. In this note, we characterize all bipartite graphs with a unique perfect matching whose adjacency matrices have inverses diagonally similar to non-negative matrices, which settles an open problem of Godsil on inverses of bipartite graphs in [Godsil, Inverses of Trees, Combinatorica 5 (1985) 33-39]. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02099683
Volume :
38
Issue :
5
Database :
Complementary Index
Journal :
Combinatorica
Publication Type :
Academic Journal
Accession number :
133453230
Full Text :
https://doi.org/10.1007/s00493-016-3502-y