一类 2-树的双变量匹配多项式
The Bivariate Matching Polynomial of a Class of 2-Tree
DOI: 10.12677/AAM.2024.1311482, PDF,   
作者: 韩军：绍兴文理学院数理信息学院，浙江 绍兴
关键词: 2-树；匹配多项式；匹配矩阵；Hosoya指数；2-Tree； Matching Polynomial； Matching Matrix； Hosoya Index
摘要: 图的单变量匹配多项式是图的匹配生成函数的等价形式之一，Farrell引入的图的双变量匹配多项式是图的单变量匹配多项式的推广。本文研究了一类2-树的双变量匹配多项式，利用匹配矩阵行列式的一种特殊展开形式得到该类2-树的双变量匹配多项式的显示表达式，进一步,获得了相应的Hosoya指数。
Abstract: The univariate matching polynomial of a graph is one of the equivalent forms of the graph matching generating function. The bivariate matching polynomial of a graph introduced by Farrell is a generalization of the univariate matching polynomial of a graph. This paper studies the bivariate matching polynomial of a class of 2-trees. By using a special expansion form of the determinant of the matching matrix, the explicit expression of the bivariate matching polynomial of this class of 2-trees is obtained. Further, the corresponding Hosoya index is obtained.
文章引用：韩军. 一类 2-树的双变量匹配多项式[J]. 应用数学进展, 2024, 13(11): 5001-5008. https://doi.org/10.12677/AAM.2024.1311482

参考文献

[1] Farrell, E.J. and Wahid, S.A. (1986) Matching Polynomials: A Matrix Approach and Its Applications. Journal of the Franklin Institute, 322, 13-21.
https://doi.org/10.1016/0016-0032(86)90072-4
[2] Heilmann, O.J. and Lieb, E.H. (1972) Theory of Monomer-Dimer Systems. Communications in Mathematical Physics, 25, 190-232.
[3] Hosoya, H. (1971) Topological Index. A Newly Proposed Quantity Characterizing the Topolog- ical Nature of Structural Isomers of Saturated Hydrocarbons. Bulletin of the Chemical Society of Japan, 44, 2332-2339.
https://doi.org/10.1246/bcsj.44.2332
[4] Harary, F. and Palmer, E.M. (1968) On acyclic simplicial complexes. Mathematika, 15, 115- 122.
https://doi.org/10.1112/s002557930000245x
[5] Arnborg, S. and Proskurowski, A. (1986) Characterization and Recognition of Partial 3-Trees. SIAM Journal on Algebraic Discrete Methods, 7, 305-314.
https://doi.org/10.1137/0607033
[6] Farrell, E.J. (1979) An Introduction to Matching Polynomials. Journal of Combinatorial The- ory, Series B, 27, 75-86.
https://doi.org/10.1016/0095-8956(79)90070-4
[7] Vein, R. and Dale, P. (2006) Determinants and Their Applications in Mathematical Physics. Springer.
[8] Zhang, F.Z. (2006) The Schur Complement and Its Applications. Springer.

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