A simple formula for the number of spanning trees of line graphs

H Gong, X Jin - Journal of Graph Theory, 2018 - Wiley Online Library
Suppose is a loopless graph and is the graph obtained from G by subdividing each of its
edges k () times. Let be the set of all spanning trees of G, be the line graph of the graph and …

The Homfly and dichromatic polynomials

X Jin, F Zhang - Proceedings of the American Mathematical Society, 2012 - ams.org
In this paper, we first associate a plane graph with an oriented link via replacing each edge
of the graph by an alternatingly oriented 2-tangle. Then we establish a relation between the …

The Yamada polynomial of spatial graphs obtained by edge replacements

M Li, F Lei, F Li, A Vesnin - Journal of Knot Theory and Its …, 2018 - World Scientific
We present formulae for computing the Yamada polynomial of spatial graphs obtained by
replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs …

[HTML][HTML] A Method for Calculating the Reliability of 2-Separable Networks and Its Applications

J Liang, H Zhao, S Xie - Axioms, 2024 - mdpi.com
This paper proposes a computational method for the reliability of 2-separable networks.
Based on graph theory and probability theory, this method simplifies the calculation process …

[HTML][HTML] 一类连通图的Tutte 多项式

祁禄 - Advances in Applied Mathematics, 2023 - hanspub.org
近年来, 随着拓扑学家对纽结理论的深入研究, 空间图理论逐渐成为学者们的研究热点. Tutte
多项式在空间图理论中具有重要地位, 本文利用缩边与减边的性质, 借助二元的数学归纳法计算 …

A general method for computing the Homfly polynomial of DNA double crossover 3-regular links

M Li, Q Deng, X Jin - Plos one, 2015 - journals.plos.org
In the last 20 years or so, chemists and molecular biologists have synthesized some novel
DNA polyhedra. Polyhedral links were introduced to model DNA polyhedra and study …

Log-concavity and zeros of the Alexander polynomial

A Stoimenow - Bulletin of the Korean Mathematical Society, 2014 - koreascience.kr
LOG-CONCAVITY AND ZEROS OF THE ALEXANDER POLYNOMIAL 1. Introduction In this
paper we will treat the Alexander polynomial ∆(t) Page 1 Bull. Korean Math. Soc. 51 (2014) …

The architecture and the Jones polynomial of polyhedral links

X Jin, F Zhang - Journal of mathematical chemistry, 2011 - Springer
In this paper, we first recall some known architectures of polyhedral links (Qiu and Zhai in J
Mol Struct (THEOCHEM) 756: 163–166, 2005; Yang and Qiu in MATCH Commun Math …

Hoste's conjecture and roots of link polynomials

A Stoimenow - Annals of Combinatorics, 2018 - Springer
In relation to a conjecture of Hoste on the roots of the Alexander polynomial of alternating
knots, we prove that any root z of the Alexander polynomial of a 2-bridge (rational) knot or …

[HTML][HTML] The number of spanning trees of a family of 2-separable weighted graphs

H Gong, S Li - Discrete Applied Mathematics, 2017 - Elsevier
Based on electrically equivalent transformations on weighted graphs, in this paper, we
present a formula for computing the number of spanning trees of a family of 2-separable …