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Journal of Applied Mathematics and Computing

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21-11-2019 | Original Research

Resistance distance-based graph invariants and the number of spanning trees of linear crossed octagonal graphs

Authors: Jing Zhao, Jia-Bao Liu, Sakander Hayat

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2020

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Abstract

Resistance distance is a novel distance function, also a new intrinsic graph metric, which makes some extensions of ordinary distance. Let \(O_n\) be a linear crossed octagonal graph. Recently, Pan and Li (Int J Quantum Chem 118(24):e25787, 2018) derived the closed formulas for the Kirchhoff index, multiplicative degree-Kirchhoff index and the number of spanning trees of \(H_n\). They pointed that it is interesting to give the explicit formulas for the Kirchhoff and multiplicative degree-Kirchhoff indices of \(O_n\). Inspired by these, in this paper, two resistance distance-based graph invariants, namely, Kirchhoff and multiplicative degree-Kirchhoff indices are studied. We firstly determine formulas for the Laplacian (normalized Laplacian, resp.) spectrum of \(O_n\). Further, the formulas for those two resistance distance-based graph invariants and spanning trees are given. More surprising, we find that the Kirchhoff (multiplicative degree-Kirchhoff, resp.) index is almost one quarter to Wiener (Gutman, resp.) index of a linear crossed octagonal graph.

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Title: Resistance distance-based graph invariants and the number of spanning trees of linear crossed octagonal graphs
Authors: Jing Zhao
Jia-Bao Liu
Sakander Hayat
Publication date: 21-11-2019
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2020
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-019-01306-6

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