On the nullity of bicyclic graphs
On the nullity of bicyclic graphs
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DOI：
10.1016/j.laa.2011.01.006
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发表时间：
2005-10
影响因子：
1.1
通讯作者：
Tan Xuezhong;Bolian Liu
中科院分区：
文献类型：
--
作者：
Tan Xuezhong;Bolian Liu
图G的零度记为η（G），是指图G的谱中特征值零的重数。如果G是n阶简单图，且G不同构于nK 1，则η（G）<$n-2.得到了达到上界n-2和第二上界n-3的极图。本文刻画了零度为n-4的图。并进一步讨论了具有最大零度的三圈图。
The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in its spectrum. It is known that η(G)⩽n-2 if G is a simple graph on n vertices and G is not isomorphic to nK1. The extremal graphs attaining the upper bound n-2 and the second upper bound n-3 have been obtained. In this paper, the graphs with nullity n-4 are characterized. Furthermore the tricyclic graphs with maximum nullity are discussed.