不含偶圈双圈图的极小斜能量
Minimal skew energies of oriented bicyclic graphs without even cycles
肖毛 1王文环1
作者信息
- 1. 上海大学理学院数学系,上海200444
- 折叠
摘要
令G为简单连通图.给图G的每条边赋予一个方向,得到的有向图,记为Gσ.有向图Gσ的斜能量Es(Gσ)定义为Gσ的斜邻接矩阵特征值的绝对值之和.令Bon表示顶点个数为n不含偶圈的双圈图的集合.考虑了Bon中图依斜能量从小到大的排序问题.利用有向图斜能量的积分公式和实分析的方法,当n≥156和155≥n≥12时,分别得到了Bon中具有最小、次二小和次三小斜能量的双圈图.
Abstract
Let G be a simple connected graph.By assigning an orientation to each edge of G,we obtained an oriented graph Gσ.The skew energy Es(Gσ) of an oriented graph Gσ is defined as the sum of the absolute eigenvalues of the skew adjacency matrix for Gσ.Let Bon be the set of bicyclic graphs without even cycles having n vertices.The ordering of graphs in Bon in terms of their minimal skew energies was considered.By employing the integral formula of skew energy and knowledge of real analysis,we deduced the first three graphs with minimal skew energies in Bon for n ≥ 156 and 155 ≥ n ≥ 12,respectively.
关键词
有向图/双圈图/斜能量Key words
oriented graphs/bicyclic graphs/skew energy引用本文复制引用
基金项目
国家自然科学基金(11001166)
上海市重点学科建设基金(S30104)
出版年
2014
NETL
NSTL
维普
万方数据