A Characterization Of Graphs G With Nullity Vertical Bar V(G)Vertical Bar-2m(G)+2c(G)

By vertical bar V(G)vertical bar, vertical bar E(G)vertical bar, eta(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, n(G) <= IV (G) - 2m(G) + 2c(G), where c(G) = vertical bar E(G)vertical bar - vertical bar V(G)vertical bar + theta(G), theta(G) being the number of connected components of G. In this paper graphs G that satisfy the equality eta(G) = vertical bar V(G)vertical bar - 2m(G) + 2c(G) are characterized. (C) 2014 Elsevier Inc. All rights reserved.