CHEN Weinan,WEI Shouliu*,YAN Shiyong,et al.Atom-bond connectivity index in a random polygonal chain[J].Journal of Yanbian University,2020,46(01):20-23.
随机多边形网格链图的ABC指数
- Title:
- Atom-bond connectivity index in a random polygonal chain
- 文章编号:
- 1004-4353(2020)01-0020-04
- Keywords:
- ABC index; expected value; polygonal chain; average value
- 分类号:
- O157.5
- 文献标志码:
- A
- 摘要:
- 针对一类多边形网格链图,利用概率和递归的方法研究了其ABC指数的计算问题,并给出了ABC指数的数学期望表达式.根据该表达式,计算了含有n个多边形的所有网格链图ABC指数的平均值.
- Abstract:
- For a type of polygonal chain, the calculation problem about the ABC index was studied by the methods of probability and recursion. We obtain an exact formula for the expected value of ABC index in a random polygonal chain. Based on the formula above, we present the average value of the ABC index with respect to all the polygonal chains with n polygons.
参考文献/References:
[1] WIENER H. Structural determination of paraffin boiling points[J]. J Amer Chem Soc, 1947,69:17-20.
[2] GUTMAN I. Degree -based topological indices[J]. Croat Chem Acta, 2013,86(4):351-361.
[3] ESTRADA E, TORRES L, RODRIGUEZ L, et al. An atom -bond connectivity index: modelling the enthalpy of formation of alkanes[J]. Indian J Chem, 1998,37(A):849-855.
[4] ESTRADA E. Atom -bond connectivity and the energetic of branched alkane[J]. Chem Phys Lett, 2008,463:422-425.
[5] FURTULA B, GRAOVAC A, VUKICEVIC D. Atom -bond connectivity index of trees[J]. Discrete Appl Math, 2009,157:2828-2835.
[6] XING R, ZHOU B, DU Z. Further results on atom -bond connectivity index of trees[J]. Discrete Appl Math, 2010,158:1536-1545.
[7] LIN W, LIN X, GAO T, et al. Proving a conjecture of Gutman concerning trees with minimal ABC index[J]. MATCH Commun Math Comput Chem, 2013,69:549-557.
[8] LIN W, GAO T, CHEN C, et al. On the minimal ABC index of connected graphs with given degree sequence[J]. MATCH Commun Math Comput Chem, 2013,69:571-578.
[9] GAN L, LIU B, YOU Z. The ABC index of trees with given degree sequence[J]. MATCH Commun Math Comput Chem, 2012,68:137-145.
[10] CHEN J, GUO X. The atom -bond connectivity index of chemical bicyclic graphs[J]. Appl Math J Chinese Uni, 2012,27(2):243-252.
[11] 陈锦松,刘剑萍.双圈图的原子键连通性指数[J].广西师范学院学报(自然科学版),2011,28(2):8-11.
[12] CHEN J, LIU J, GUO X. Some upper bounds for the atom -bond connectivity index of graphs[J]. Appl Math Lett, 2012,25(7):1077-1081.
[13] CHEN J, GUO X. Extreme atom -bond connectivity index of graphs[J]. MATCH Commun Math Comput Chem, 2011,65:713-722.
[14] 陈锦松,刘剑萍.图的移边变换与原子键连通性指数的关系[J].数学的实践与认识,2013,43(22):162-165.
[15] KE X. Atom -bond connectivity index of benzenoid systems and fluoranthene congeners[J]. Poly Aroma Comp, 2012,32:27-35.
[16] 魏首柳,柯小玲.自由边界条件下的两类网格图的ABC指标[J].廊坊师范学院学报,2015,15(5):9-12.
[17] 柯小玲.曲面上的四边形网格图的ABC指标[J].闽江学院学报,2017,29(2):1-5.
[18] 武琳,胡玉梅.图的ABC指标与直径[J].河北科技大学学报,2016,37(6):552-555.
[19] 杨世永,魏首柳,刘天,等.随机聚环戊二烯链图的ABC指标[J].河南工程学院学报,2019,31(2):77-80.
[20] KE X, WEI S, HUAN J. The atom -bond connectivity and geometric -arithmetic indices in random polyphenyl and spiro chains[J]. Poly Arom Comp, 2019,32:27-35.
备注/Memo
收稿日期: 2019-11-30 *通信作者: 魏首柳(1978—),男,博士,教授,研究方向为图论及其应用.
基金项目: 福建省自然科学基金资助项目(2015J01589); 教育部大学生创新创业项目(201910395009)