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Kirchhoff index, multiplicative degree‐Kirchhoff index and spanning trees of the linear crossed hexagonal chains
Author(s) -
Pan Yingui,
Li Jianping
Publication year - 2018
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.25787
Subject(s) - mathematics , multiplicative function , degree (music) , eigenvalues and eigenvectors , tridiagonal matrix , combinatorics , laplace operator , order (exchange) , hexagonal crystal system , matrix (chemical analysis) , index (typography) , laplacian matrix , wiener index , diagonal , mathematical analysis , geometry , physics , crystallography , quantum mechanics , materials science , chemistry , graph , finance , acoustics , economics , composite material , world wide web , computer science
Let H n be a linear crossed hexagonal chain with n crossed hexagonals. In this article, we find that the Laplacian (resp. normalized Laplacian) spectrum of H n consists of the eigenvalues of a symmetric tridiagonal matrix of order 2 n + 1 and a diagonal matrix of order 2 n + 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 H n are derived. Finally, we show that the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index of H n is approximately one quarter of its Wiener (resp. Gutman) index.