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 $3n$ ($n\ge 2$) hexagons shown in Fig. 2(a). In this paper, we give the explicit expression of the characteristic polynomial ${\mathrm{\Phi }}_A(E_n^2,x)$. 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.