|
|
一类花图f(Cm,Fn)的Tutte多项式
|
Abstract:
图多项式不变量已被证实在量子化学和生物信息方面有重要的应用。著名的图多项式不变量之一是Tutte多项式，它包含了关于图结构的各种有趣的信息。本文借助Tutte多项式的一些性质对一类花图f(Cm,Fn)进行研究，最终得到这类花图Tutte多项式的具体表达式。
Polynomial graph invariants have been confirmed to have important applications in quantum chemistry and biological information. One of the famous polynomial graph invariants is the Tutte polynomial which gives multifarious interesting information about the graph structure. In this pa-per, with the help of some properties of Tutte polynomials, a class of flower diagrams f(Cm,Fn) is studied, and finally the specific expressions of Tutte polynomials of this kind of flower diagrams are obtained.
| [1] | Tutte, W.T. (1954) A Contribution to the Theory of Chromatic Polynomials. Canadian Journal of Mathematics, 6, 80-91. https://doi.org/10.4153/CJM-1954-010-9 |
| [2] | Jaeger, F. (1988) Tutte Polynomials and Link Polynomials. Pro-ceedings of the American Mathematical Society, 103, 647-654. |
| [3] | Ellis-Monaghan, A.J. and Merino, C. (2008) Graph Polynomials and Their Applications I: The Tutte Polynomial. In: Dehmer, M., Ed., Structural Analysis of Complex Net-works, Birkh？user, Boston, 219-255.
https://doi.org/10.1007/978-0-8176-4789-6_9 |
| [4] | Brennan, C., Mansour, T. and Mphako-Banda, E. (2013) Tutte Polynomials of Wheels via Generating Functions. Bulletin of the Iranian Mathematical Society, 39, 881-891. |
| [5] | Chen, H. and Deng, H. (2016) Tutte Polynomial of Scale-Free Networks. Journal of Statistical Physics, 163, 714-732.
https://doi.org/10.1007/s10955-016-1465-4 |
| [6] | Chen, H. and Guo, Q. (2019) Tutte Polynomials of Alternating Polycyclic Chains. Journal of Mathematical Chemistry, 57, 2248-2260. https://doi.org/10.1007/s10910-019-01069-2 |
| [7] | Ren, H.Z., Xu, D.Q. and Yang, W.L. (2021) The Tutte Polyno-mial of Catacondesed Benzenoid Systems. Journal of Mathematical Chemistry, 59, 529-541. https://doi.org/10.1007/s10910-020-01205-3 |
| [8] | Kumala, I.S. and Salman, A.N.M. (2015) The Rainbow Connec-tion Number of a Flower (Cm, Kn) and a Flower (C3, Fn) Graph. Procedia Computer Science, 74, 168-172. https://doi.org/10.1016/j.procs.2015.12.094 |
| [9] | Pranata, P.Y., Kiftiah, M. and Fran, F. (2020) Star Number of Flower Graphs. AIP Conference Proceedings, 2268, 405-415. https://doi.org/10.1063/5.0018116 |
| [10] | Bolloba, B. (1998) Modern Graph Theory. Springer, Berlin. |
| [11] | Kung, J.P.S., Noy, M. and Welsh, D. (2004) Special Issue on the Tutte Polynomial. Advances in Applied Mathematics, 32, 1-2. https://doi.org/10.1016/S0196-8858(03)00073-3 |
| [12] | Hall, A. (2014) The Tutte Polynomial Formula for the Class of Twisted Wheel Graphs. |
