Abstract

The spectral moments of the edge adjacency matrix and adjacency matrix recently have been successfully employed in quantitative structure–property relationship and quantitative structure–activity relationship studies of alkanes, alkyl halides, benzyl alcohols,cycloalkanes and benzenoid hydrocarbons. Let G be a molecular graph with n vertices, m edges and G(L) be a line graph. Both graphs G and G(L) can be represented by their adjacency matrixes A and E, respectively. The eigenvalues of G and G(L) are denoted by, ${\lambda }_1⩾{\lambda }_2⩾\cdots ⩾{\lambda }_n$ and ${\gamma }_1⩾{\gamma }_2⩾\cdots ⩾{\gamma }_n,$ respectively. The Estrada index A and G(L) are defined as $EE(G)={\sum }_{i=1}^n{e}^{{\lambda }_i}$ and $EE(G(L))={\sum }_{i=1}^n{e}^{{\gamma }_i}.$ In this paper, we examined both Estrada indices with spectral moments of the edge adjacency matrix and adjacency matrix of benzenoid hydrocarbons. These theoretical conclusions provide practical guiding significance for pharmaceutical engineering, complex network and quantify the degree of folding of long organic molecules.

摘要

边缘邻接矩阵和邻接矩阵的光谱矩最近已成功应用于烷烃、卤代烷、苯甲醇、环烷烃和苯烃的定量构效关系和定量构效关系研究。设G为具有n个顶点、m条边的分子图， G ( L ) 为折线图。图G和G ( L ) 都可以分别用它们的邻接矩阵A和E来表示。G和G ( L _) 表示为，${\lambda }_1⩾{\lambda }_2⩾\cdots ⩾{\lambda }_n$和${\gamma }_1⩾{\gamma }_2⩾\cdots ⩾{\gamma }_n,$分别。Estrada 指数A和G ( L ) 定义为$乙乙(G)={\sum }_{\mathrm{一世}=1}^n{e}^{{\lambda }_{\mathrm{一世}}}$和$乙乙(G(\mathrm{大号}))={\sum }_{\mathrm{一世}=1}^n{e}^{{\gamma }_{\mathrm{一世}}}.$在本文中，我们检查了 Estrada 指数与边缘邻接矩阵和苯烃类邻接矩阵的谱矩。这些理论结论为制药工程、复杂网络和量化长有机分子的折叠程度提供了现实指导意义。