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Inverses of Bipartite Graphs.
- 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