Results on the Estrada Indices of Benzenoid Hydrocarbons

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.

Keywords:

• Benzenoid hydrocarbons
• Estrada index
• hexagons
• line graph
• molecular graph
• spectral moments

Disclosure statement

There are no conflicts of interest.