A characterization of graphs G with nullity |V(G)|–2m(G)＋2c(G)

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Title:	A characterization of graphs G with nullity \|V(G)\|–2m(G)＋2c(G)
Authors:	Song, Ya-zhi;Song, Xiao-qiu;Tam Bit-Shun
Keywords:	Nullity;Rank;Matching number
Date:	2015-01-15
Issue Date:	2015-07-22 18:18:09 (UTC+8)
Abstract:	By \|V(G)\|, \|E(G)\|, η(G), and m(G) we denote respectively the order, the number of edges, the nullity, and the matching number of a (simple) graph G. Recently Wang and Wong have proved that for every graph G , η(G)≤\|V(G)\|−2m(G)+2c(G), where c(G)=\|E(G)\|−\|V(G)\|+θ(G), θ(G) being the number of connected components of G. In this paper graphs G that satisfy the equality η(G)=\|V(G)\|−2m(G)+2c(G) are characterized.
Relation:	Linear Algebra and its Applications 465, pp.363-375
DOI:	10.1016/j.laa.2014.09.034
Appears in Collections:	[Department of Applied Mathematics and Data Science] Journal Article

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