不含偶圈双圈图的极小斜能量

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^\sigma. 有向图G^\sigma的斜能量E_{s}(G^{\sigma})定义为G^\sigma的斜邻接矩阵特征值的绝对值之和. 令\mathcal{B}^\circ_{n}表示顶点个数为n不含偶圈的双圈图的集合. 考虑了\mathcal{B}^\circ_{n}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 \geq 156和155 \geq n\geq 12时, 分别得到了\mathcal{B}^\circ_{n}中具有最小、次二小和次三小斜能量的双圈图.

Minimal skew energies of oriented bicyclic graphs without even cycles

Let G be a simple connected graph. By assigning an orientation to each edge of G, we obtained an oriented graph G^{\sigma}. The skew energy E_{s}(G^{\sigma}) of an oriented graph G^\sigma is defined as the sum of the absolute eigenvalues of the skew adjacency matrix for G^\sigma. Let \mathcal{B}^\circ_{n} be the set of bicyclic graphs without even cycles having n vertices. The ordering of graphs in \mathcal{B}^\circ_{n} 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 threegraphs with minimal skew energies in \mathcal{B}^\circ_{n} for n\geq 156 and 155 \geq n\geq 12, respectively.