有向多边形的二部图能量。
Digraph Energy of Directed Polygons.
机构信息
School of Mathematics and Statistics, Qinghai Normal University, Xining, 810001,China.
出版信息
Comb Chem High Throughput Screen. 2022;25(3):496-499. doi: 10.2174/1386207323666201111125732.
BACKGROUND
The energy E(G)of Graph G is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. In theoretical chemistry, within the Huckel molecular orbital (HMO) approximation, the energy levels of the π-electrons in molecules of conjugated hydrocarbons are related to the energy of the molecular graphs.
OBJECTIVE
The digraph with maximum digraph energy in a class of graphs is found.
METHODOLOGY
Let Δ be the set consisting of digraphs with n vertices and each cycle having length = 2mod(4). The set of all the n-order directed hollow k-polygons in Δ based on a - polygon G is denoted by H(G).
RESULTS
In this research, by using the quasi-order relation over Δ and the characteristic polynomials of digraphs, we describe the directed hollow k-polygon with the maximum digraph energy in H(G).
CONCLUSION
The n-order oriented hollow k-polygon with the maximum digraph energy among H_k (G) only contains a cycle. Moreover, such a cycle is the longest one produced in G.
背景
图 G 的能量 E(G)定义为其邻接矩阵的特征值的绝对值之和。在理论化学中，在休克尔分子轨道（HMO）近似中，共轭碳氢化合物分子中π 电子的能级与分子图的能量有关。
目的
在一类图中找到具有最大图能量的有向图。
方法
令 Δ 为顶点数为 n 的有向图集合，每个环的长度=2mod(4)。基于 - 多边形 G 的所有 n 阶有向空心 k-多边形的集合记为 H(G)。
结果
在这项研究中，通过使用 Δ 上的拟序关系和有向图的特征多项式，我们描述了 H(G)中具有最大图能量的有向空心 k-多边形。
结论
在 H_k (G)中，具有最大图能量的 n 阶有向空心 k-多边形仅包含一个环。此外，这样的环是 G 中产生的最长环。
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