The Characteristic Polynomial of a kind of Hexagonal System and its Application

Abstract

The hexagonal system considered here, denoted by \({E}_n^2\), is formed by \(3n\) (\(n \geq 2\)) hexagons shown in Fig. 2(a). In this paper, we give the explicit expression of the characteristic polynomial \(\Phi_A({E}_n^2, x)\). Subsequently, we obtain the multiplicity of eigenvalues \(+1\), the spectral radius, and the nullity of \({E}_n^2\). Furthermore, the energy, Estrada index, and the number of Kekulé structures of \({E}_n^2\) are determined.