The Laplacian spectrum, Kirchhoff index and complexity of the linear heptagonal networks

Abstract

Let H n be the linear heptagonal networks with 2n heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of H n , we utilize the decomposition theorem. Thus, the Laplacian spectrum of H n is created by eigenvalues of a pair of matrices: L A and L S of order number 5n + 1 and 4n + 1, respectively. On the basis of the roots and coefficients of their characteristic polynomials of L A and L S , we not only get the explicit forms of Kirchhoff index, but also corresponding total complexity of H n .