An upper bound for the nullity of a bipartite graph in terms of its maximum degree

作者：Song, Ya-zhi; Song, Xiao-qiu^*; Zhang, Mingcui

来源：Linear and Multilinear Algebra, 2016, 64(6): 1107-1112.

DOI：10.1080/03081087.2015.1072530

• reduced graphs
• maximum degree
• rank
• nullity
• 05C50

Let
[GRAPHICS]
be a connected undirected graph without loops and multiple edges. The graph
[GRAPHICS]
is said to be reduced if distinct vertices of
[GRAPHICS]
have distinct neighbours in
[GRAPHICS]
. The nullity
[GRAPHICS]
of
[GRAPHICS]
is the multiplicity of
[GRAPHICS]
as an eigenvalue of the adjacency matrix of
[GRAPHICS]
. By
[GRAPHICS]
and
[GRAPHICS]
, we respectively denote the order and the maximum degree of
[GRAPHICS]
. In this note, it is proved that
[GRAPHICS]
if
[GRAPHICS]
is a reduced bipartite graph and the graphs attaining equality are characterized.

• 出版日期2016-6
• 单位中国矿业大学（北京）