Abstract

Let G be a molecular graph with n vertices, m edges and G(L) be a line graph. Both G and L can be represented by their adjacency matrices A and E, respectively. The eigenvalues of G and L are denoted by, ${\lambda }_1⩾{\lambda }_2⩾\dots ⩾{\lambda }_n$ and ${\gamma }_1⩾{\gamma }_2⩾\dots ⩾{\gamma }_n,$ respectively. The Estrada index A and L are defined as $EE(G)={\sum }_{i=1}^n{e}^{{\lambda }_i}$ and $EE(L)={\sum }_{i=1}^n{e}^{{\gamma }_i}.$ In this article, we present some new lower and upper bounds for the Estrada index molecular and line graphs of phenylenes.

中文翻译：

---

亚苯基 Estrada 指数的新界限

摘要

设G为具有n个顶点、m条边的分子图， G ( L ) 为折线图。G和L都可以分别用它们的邻接矩阵A和E来表示。G和L的特征值表示为，${\lambda }_1⩾{\lambda }_2⩾\dots ⩾{\lambda }_n$和${\gamma }_1⩾{\gamma }_2⩾\dots ⩾{\gamma }_n,$分别。Estrada 指数A和L定义为$乙乙(G)={\sum }_{\mathrm{一世}=1}^n{e}^{{\lambda }_{\mathrm{一世}}}$和$乙乙(\mathrm{大号})={\sum }_{\mathrm{一世}=1}^n{e}^{{\gamma }_{\mathrm{一世}}}.$在本文中，我们提出了一些新的 Estrada 指数分子和亚苯基折线图的下限和上限。