Kirchhoff index, multiplicative degree‐Kirchhoff index and spanning trees of the linear crossed hexagonal chains

Let Hn be a linear crossed hexagonal chain with n crossed hexagonals. In this article, we find that the Laplacian (resp. normalized Laplacian) spectrum of Hn consists of the eigenvalues of a symmetric tridiagonal matrix of order 2n + 1 and a diagonal matrix of order 2n + 1. Based on the properties of these matrices, significant closed formulas for the Kirchhoff index, multiplicative degree‐Kirchhoff index and the number of spanning trees of Hn are derived. Finally, we show that the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index of Hn is approximately one quarter of its Wiener (resp. Gutman) index. Based on the decomposition theorem of the Laplacian (resp. normalized Laplacian) polynomial, significant closed formulas for the Kirchhoff index, multiplicative degree‐Kirchhoff index, and the number of spanning trees are derived. In addition, the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index is found to be approximately one quarter of its Wiener (resp. Gutman) index.