Computing the Energy and Estrada Index of Different Molecular Structures

Abstract

Graph energy is an invariant that is derived from the spectrum of the adjacency matrix of a graph. Graph energy is actually the absolute sum of all the eigenvalues of the adjacency matrix of a graph i.e. $E={\displaystyle {\sum }_{i=1}^n\left|{\lambda }_i\right|}$ , and the Estrada index of a graph $G$ is elaborated as $\text{EE}\left(G\right)={\displaystyle {\sum }_{i=1}^n{e}^{{\lambda }_i}}$ , where, ${\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n$ are the eigenvalues of the adjacency matrix of a graph. In this paper, energy $E\left(G\right)$ and Estrada index $\text{EE}\left(G\right)$ of different molecular structures are obtained and also established inequalities among the exact and estimated values of energies and Estrada index of ${\text{TUC}}_4{C}_8$ nanosheet and naphthalene.