The complete forcing number of polyphenyl systems
The complete forcing number of polyphenyl systems
复制标题
聚苯体系的完整受力数
DOI：
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发表时间：
2016
影响因子：
1.3
通讯作者：
Haizheng Yu
中科院分区：
文献类型：
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作者：
Bingjie Liu;Hong Bian;Haizheng Yu
“强迫”的概念在图论中的着色、定向、测地学和控制集，以及组合数学中的拉丁方、区组设计和Steiner系统[D. Donovan，E. S.. Mahmoodian角Ramsay，A. P. Street，Defining sets in combinatorics：A survey，in：C. D. Wensley（Ed.），《组合数学概论》，剑桥大学出版社，2003年，页。115 - 174]。近年来，对完美匹配的强迫已经引起了越来越多的研究者的关注。图G的完美匹配M的强制集是.M的一个子集，不包含在G的其他完美匹配中。Vukičević等人提出的G的全球强迫集，是E（G）的一个子集，在这个子集上G的任意两个不同的完美匹配都有明显的限制。结合上述“强迫”和“全球”的想法。Xu.et al. in [Complete forcing numbers of catacondensed benzenoid，J. Combin. Optim。29.（2015）803 - 814.]引入了G的一个完全强制集，定义为E（G）的一个子集，在这个子集上，G的任何完美匹配M的限制是M的一个强制集。完备强迫集的最小基数是G的完备强迫数。本文给出了几类多苯基体系完全强迫数的显式表达式。
The idea of “forcing” has long been used in many research fields, such as.colorings, orientations, geodetics and dominating sets in graph theory, as well as Latin.squares, block designs and Steiner systems in combinatorics [D. Donovan, E. S..Mahmoodian, C. Ramsay, A. P. Street, Defining sets in combinatorics: A survey, in: C..D. Wensley (Ed.), Surveys in Combinatorics, Cambridge Univ. Press, 2003, pp..115174]. Recently, the forcing on perfect matchings has been attracting more.researchers’ attention. A forcing set of a perfect matching M of a graph G is a subset of.M contained in no other perfect matchings of G. A global forcing set of G, introduced by.Vukičević et al., is a subset of E(G) on which there are distinct restrictions of any two.different perfect matchings of G. Combining the above “forcing” and “global” ideas. Xu.et al. in [Complete forcing numbers of catacondensed benzenoid, J. Combin. Optim. 29.(2015) 803814.] introduced a complete forcing set of G defined as a subset of E(G) on.which the restriction of any perfect matching M of G is a forcing set of M. The minimum.cardinality of complete forcing sets is the complete forcing number of G. In this paper,.we give the explicit expressions for the complete forcing number of several classes of.polyphenyl systems.