零度为$n-7$的双圈符号图

A Characterization of Bicyclic Signed Graphs with Nullity $n-7$

中文关键词:  零度  符号图  双圈图  邻接矩阵

英文关键词:nullity  signed graph  bicyclic graph  adjacency matrix

中文摘要:

      设$\Gamma$为符号图，其邻接矩阵为$A(\Gamma)$. $\Gamma$的零度指的是其邻接$A(\Gamma)$矩阵的零特征值的重数. 本文刻画了所有的零度为$n-7$ 的$n$ 阶连通双圈（符号)图.

英文摘要:

      Let $\Gamma$ be a signed graph and $A(\Gamma)$ be the adjacency matrix of $\Gamma$. The nullity of $\Gamma$ is the multiplicity of eigenvalue zero in the spectrum of $A(\Gamma)$. In this paper, the connected bicyclic signed graphs (including simple bicyclic graphs) of order $n$ with nullity $n-7$ are completely characterized.