The normalized Laplacians, degree-Kirchhoff index and the spanning trees of hexagonal Mobius graphs

Let HMn be a hexagonal Mobius graph of length n. In this paper, due to the normalized Laplacian polynomial decomposition theorem, we obtain that the normalized Laplacian spectrum of HMn consists of the eigenvalues of two symmetric quasi-tridiagonal matrices L-A and L-S of order 2n. Finally, by applying the relationship between the roots and coefficients of the characteristic polynomials of the above two matrices, explicit closed formulas of the degree-Kirchhoff index and the number of spanning trees of HMn are given in terms of the index n. (C) 2019 Elsevier Inc. All rights reserved.