不含偶圈双圈图的极小斜能量

Minimal skew energies of oriented bicyclic graphs without even cycles

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G~σ.有向图G~σ的斜能量E_s(G~σ)定义为G~σ的斜邻接矩阵特征值的绝对值之和.令B_n^o表示顶点个数为n不含偶圈的双圈图的集合.考虑了B_n^o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B_n^o中具有最小、次二小和次三小斜能量的双圈图.

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, resoectivelv.