中山大学学报自然科学版 ›› 2016, Vol. 55 ›› Issue (6): 57-63.

• 研究论文 • 上一篇    下一篇

零度为 n-4 的图的特征多项式

吴廷增1, 冯立华2, 马海成1   

  1. 1. 青海民族大学数学与统计学院, 青海 西宁 810007;
    2. 中南大学数学系, 湖南 长沙 410083
  • 收稿日期:2015-11-28 出版日期:2016-11-25 发布日期:2016-11-25
  • 通讯作者: 吴廷增(1978年生),男;研究方向:数学化学、图的匹配理论和计算机网络;Email:mathtzwu@163.com

On the characteristic polynomials of graphs with nullity n-4

WU Tingzeng1, FENG Lihua2, MA Haicheng1   

  1. 1. School of Mathematics and Statistics, Qinghai Nationalities University, Xining 810007, China;
    2. Department of Mathematics, Central South University, Changsha 410083, China
  • Received:2015-11-28 Online:2016-11-25 Published:2016-11-25

摘要:

图的零度是指图的邻接谱中零特征根的重数。显然, n 个顶点的图G的零度等于 n 减去其邻接矩阵的秩。计算了零度为 n-4 的所有图的特征多项式。特别地, 证明了许多零度为 n-4 的图是谱唯一确定的, 并构造了许多对零度为 n-4 的同谱图。

关键词: 特征多项式, 秩, 零度, 同谱图

Abstract:

The nullity of a graph is the multiplicity of zeroes in its adjacency spectrum. And the nullity of a graph G with n vertices equals to n minus the rank of adjacency matrix of G. The characteristic polynomials of graphs with nullity n-4 is computed. In particular, it is shown that some graphs with nullity n-4 are determined by their spectra. And some pairs of cospectral graphs with nullity n-4 are presented.

Key words: characteristic polynomial, rank, nullity, cospectral graphs

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