New Bounds for the Estrada Index of Phenylenes

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.

Keywords:

• Estrada index
• hexagons
• line graph
• molecular graph
• phenylenes
• spectral moments

MATHMATICS SUBJECT CLASSIFICATION:

• 05C09
• 05C92
• 92E10

Acknowledgment

The authors would like to thanks the two anonymous reviewers for their very constructive comments that helped us to enhance the quality of this manuscript.

Disclosure statement

There are no conflicts of interest.