Abstract
Let G be a connected undirected graph without loops and multiple edges. By , and
we, respectively, denote the order, the nullity, and the matching number of G. Let
, and let
be a nonnegative integer defined as: To make G to be a bipartite connected graph at least
edges of G must be deleted from G. In this note, applying an operation called bipartite double, we prove that
for an arbitrary connected graph G. This result improves a main result in Wang and Wong [Bounds for the matching number, the edge chromatic number and the independence number of a graph in terms of rank. Disc Appl Math. 2014;166:276–281] saying that
for a connected graph G.
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Disclosure statement
No potential conflict of interest was reported by the authors.