准树图的零阶广义Randic指数

doi:10.6040/j.issn.1671-9352.0.2021.184

摘要/Abstract

摘要： 利用零阶广义Randic指数的性质,通过分析准树图的结构,确定了具有完美匹配和p个悬挂点的准树图的零阶广义Randic指数的极值,并刻画了相应的极图。

Abstract: By using the properties of the zeroth-order general Randic index and analyzing the structure of the quasi-tree graphs, the extremal values of zeroth-order general Randic indices of quasi-tree graphs with perfect matchings and p pendant vertices are determined. Furthermore, the corresponding extremal quasi-tree graphs are identified.

Key words: zeroth-order general Randic index, quasi-tree graph, perfect matching, pendant vertex

中图分类号:

O157.5

孙晓玲,高玉斌,杜建伟,任建斌. 准树图的零阶广义Randic指数[J]. 《山东大学学报(理学版)》, 2022, 57(12): 96-102.

SUN Xiao-ling, GAO Yu-bin, DU Jian-wei, REN Jian-bin. Zeroth-order general Randic index of quasi-tree graphs[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(12): 96-102.

参考文献

[1] GUTMAN I, FURTULA B. Novel molecular structure descriptors-theory and applications:I[M]. Serbia: University of Kragujevac, 2010.
[2] GUTMAN I, FURTULA B. Novel molecular structure descriptors-theory and applications:II[M]. Serbia: University of Kragujevac, 2010.
[3] TODESCHINI R, CONSONNI V. Handbook of molecular descriptors[M]. Weinheim: Wiley-VCH, 2000.
[4] RANDIC M. On characterization of molecular branching[J]. Journal of the American Chemical Society, 1975, 97:6609-6615.
[5] KIER L B, HALL L H. Molecular connectivity in chemistry and drug research[M]. New York: Academic Press, 1976.
[6] KIER L B, HALL L H. Molecular connectivity in structure-activity analysis[M]. Champaign: Research Studies Press, 1986.
[7] BOLLOBAS B, ERDOS P. Graphs of extremal weights[J]. ARS Combinatoria, 1998, 50:225-233.
[8] KIER L B, HALL L H. The nature of structure-activity relationships and their relation to molecular connectivity[J]. European Journal of Medicinal Chemistry, 1977, 12:307-312.
[9] LI Xueliang, ZHENG Jie. A unified approach to the extremal trees for different indices[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2005, 54:195-208.
[10] LI Xueliang, SHI Yongtang. A survey on the Randic index[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2008, 59:127-156.
[11] DU Jianwei, SHAO Yanling, SUN Xiaoling. The zeroth-order general Randic index of graphs with a given clique number[J]. Journal of the Korean Mathematical Society, 2020, 28:405-419.
[12] WU Renfang, CHEN Hanlin, DENG Hanyuan. On the monotonicity of topological indices and the connectivity of a graph[J]. Applied Mathematics and Computation, 2017, 298:188-200.
[13] KHALID S, ALI A. On the zeroth-order general Randic index, variable sum exdeg index and trees having vertices with prescribed degree[J]. Discrete Mathematics, Algorithms and Applications, 2018, 10: 1850015.
[14] MILOSEVIC P, MILOVANOVIC I, MILOVANOVIC E, et al. Some inequalities for general zeroth-order Randic index[J]. Filomat, 2019, 33:5249-5258.
[15] AHMEDA H, BHATTIA A A, ALI A. Zeroth-order general Randic index of cactus graphs[J]. AKCE International Journal of Graphs and Combinatorics, 2019, 16:182-189.
[16] JAMIL M K, TOMESCU I, IMRAN M, et al. Some bounds on zeroth-order general Randic index[J]. Mathematics, 2020, 8(1):98-109.
[17] SU Guifu, YAN Jingru, CHEN Zhibing, et al. Some extremal graphs with respect to the zeroth-order general Randic index[J]. Utilitas Mathematica, 2020, 114:73-98.
[18] BONDY J A, MURTY U S R. Graph theory with applications[M]. New York: Elsevier, 1976.
[19] DEHGHAN-ZADEH T, ASHRAF A R. Atom-bond connectivity index of quasi-tree graphs[J]. Rendiconti del Circolo Matematico di Palermo, 2014, 63:347-354.
[20] LI Shuchao, LI Xuechao, JING Wei. On the extremal Merrifield-Simmons index and Hosoya index of quasi-tree graphs[J]. Discrete Applied Mathematics, 2009, 157:2877-2885.
[21] LU Mei, GAO Jinwu. On the Randic index of quasi-tree graphs[J]. Journal of Mathematical Chemistry, 2007, 42: 297-310.
[22] QIAO Shengning. On the Zagreb index of quasi-tree graphs[J]. Applied Numerical Mathematics, 2010, 10:147-150.
[23] QIAO Shengning. On zeroth-order general Randic index of quasi-tree graphs containing cycles[J]. Discrete Optimization, 2010, 7:93-98.
[24] SUN Xiaoling, GAO Yubin, DU Jianwei. The harmonic index of two-trees and quasi-tree graphs[J]. Journal of Mathematical Inequalities, 2019, 13:479-493.
[25] XU Kexiang, WANG Jinlan, LIU Hongshuang. The Harary index of ordinary and generalized quasi-tree graphs[J]. Journal of Applied Mathematics and Computing, 2014, 45:365-374.
[26] SUN Xiaoling, DU Jianwei. On variable sum exdeg indices of quasi-tree graphs and unicyclic graphs[J]. Discrete Dynamics in Nature and Society, 2020, 2020:1317295.
[27] DU Jianwei, SUN Xiaoling. Quasi-tree graphs with extremal general multiplicative Zagreb indices[J]. IEEE Access, 2020, 8:194676-194684.
[28] HUA Hongbo, WANG Maolin, WANG Hongzhuan. On zeroth-order general Randic index of conjugated unicyclic graphs[J]. Journal of Mathematical Chemistry, 2007, 43:737-748.

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