设
G 是一个有完美匹配的简单连通图。若
G 的一个边子集
S 满足
G-
S 只有唯一完美匹配,则称
S 是
G 的一个反强迫集。
G 中最小的反强迫集的大小称为
G 的反强迫数。本文主要研究圈和路的卡什积图的反强迫数。根据一个图有唯一完美匹配的必要条件,我们证明了
C
3×
P
2k,
C
2K+1×
P
2,
C
4×
P 的反强迫数都为
k+1,并表明了
C
2k×
P
2 (k≥2) 的反强迫数恒为3。
Let
G be a simple connected graph with a perfect matching,
S an edge set of
G. We call
S an anti- forcing set of
G, if
G-
S contains only one perfect matching of
G. The cardinality of the minimum anti-forcing set of
G is called the anti-forcing number of
G. In this paper, we study the anti-forcing number of the Cartesian product of a cycle and a path. According to the necessity of a graph with only one perfect matching, we show that the anti-forcing numbers of
C
3×
P
2k,
C
2K+1×
P
2,
C
4×
P are all
k+1 , and the anti-forcing number of
C
2k×
P
2 (k≥2) is 3.
圈和路的卡什积图,完美匹配,反强迫数, The Cartesian Product of a Cycle and a Path Perfect Matching Anti-Forcing Numbers关于的反强迫数
张勇军,蔡金转. 关于Cm×Pk的反强迫数 On the Anti-Forcing Number of Cm×Pk[J]. 应用数学进展, 2016, 05(03): 435-442. http://dx.doi.org/10.12677/AAM.2016.53054
参考文献 (References)ReferencesKlein, D. and Randic, M. (1987) Innate Degree of Freedom of a Graph. Journal of Computational Chemistry, 8, 516-521. <br>http://dx.doi.org/10.1002/jcc.540080432Randic, M. and Klein, D. (1985) Kekule Valence Structures Revisited. Innate Degrees of Freedom of π-Electron Couplings. In: Trinajstic, N., Ed., Mathematics and Computational Concepts in Chemistry, Hor-wood/Wiley, New York, 274-282.Harary, F., Klein, D. and Zivkovic, T. (1991) Graphical Properties of Polyhexes: Perfect Matching Vector and Forcing. Journal of Mathematical Chemistry, 6, 295-306. <br>http://dx.doi.org/10.1007/BF01192587Vukicevic, D. and Trinajstic, N. (2007) On the Anti-Forcing Number of Benzenoids. Journal of Mathematical Chemistry, 42, 575-583. <br>http://dx.doi.org/10.1007/s10910-006-9133-6Deng, H. (2007) The Anti-Forcing Number of Hexagonal Chains. MATCH Communications in Mathematical and in Computer Chemistry, 58, 675-682.Deng, H. (2008) The Anti-Forcing Number of Double Hexagonal Chains. MATCH Communications in Mathematical and in Computer Chemistry, 60, 183-192.Zhang, Q., Bian, H. and Vumar, E. (2011) On the Anti-Kekule and Anti-Forcing Number of Cata-Condensed phenylenes. MATCH Communications in Mathematical and in Computer Chemistry, 65, 799-806.杨琴. 富勒烯图的反凯库勒数和反强迫数[D]: [硕士学位论文]. 兰州: 兰州大学, 2010.蒋晓艳, 程晓胜. 硼氮富勒烯图的反强迫数[J]. 湖北师范学院学报(自然科学版), 2013, 33(3): 28-30.Lovasz, L. and Plummer, M.D. (1986) Matching Theory. Annals of Discrete Mathematics Vol. 29, North-Holland, Amsterdam.