基于Wiener指数和Harary指数的泛圈图的充分条件

doi:10.15960/j.cnki.issn.1007-6093.2023.03.014

运筹学学报 ›› 2023, Vol. 27 ›› Issue (3): 169-177.doi: 10.15960/j.cnki.issn.1007-6093.2023.03.014

基于Wiener指数和Harary指数的泛圈图的充分条件

贾会才¹^,*(), 宋宏业²

1. 河南工程学院理学院, 河南郑州 451191
2. 北京第二外国语学院基础科学部, 北京 100024

收稿日期:2020-04-04 出版日期:2023-09-15 发布日期:2023-09-14
通讯作者: 贾会才 E-mail:jhc607@163.com
作者简介:贾会才, E-mail: jhc607@163.com
基金资助:
国家自然科学基金(11701148);国家自然科学基金(11801144)

Sufficient conditions on Wiener index and Harary index for pancyclic graphs

Huicai JIA¹^,*(), Hongye SONG²

1. College of Sciences, Henan University of Engineering, Zhengzhou 451191, Henan, China
2. Ministry of Basic Science, Beijing International Studies University, Beijing 100024, China

Received:2020-04-04 Online:2023-09-15 Published:2023-09-14
Contact: Huicai JIA E-mail:jhc607@163.com

摘要/Abstract

摘要：

令G是一个简单连通图。若G包含长度为3到n的所有圈, 则称图G是泛圈的。基于Wiener指数、Harary指数、距离谱半径和Harary谱半径, 提供了图G是泛圈图的充分条件, 从而建立了图的代数性质与结构性质之间的紧密联系。

关键词: 泛圈图, Wiener指数, Harary指数, 距离谱半径, Harary谱半径

Abstract:

Let G be a simple and connected graph. A graph G is pancyclic if it contains all possible cycles with length from three to the number of vertices. In this paper, we provide sufficient conditions for a graph to be pancyclic in terms of the Wiener index, the Harary index, the distance spectral radius and the Harary spectral radius of a graph, respectively. These results establish the relationship between algebraic properties and structural properties of graphs.

Key words: pancyclic graphs, Wiener index, Harary index, distance spectral radius, Harary spectral radius

中图分类号:

O221

贾会才, 宋宏业. 基于Wiener指数和Harary指数的泛圈图的充分条件[J]. 运筹学学报, 2023, 27(3): 169-177.

Huicai JIA, Hongye SONG. Sufficient conditions on Wiener index and Harary index for pancyclic graphs[J]. Operations Research Transactions, 2023, 27(3): 169-177.

图/表 2

参考文献 6

1	Wiener H . Structural determination of paraffin boiling points[J]. Journal of the American Chemical Society, 1947, 69, 17- 20. doi: 10.1021/ja01193a005
2	Ivanciuc O , Balaban T , Balaban A . Reciprocal distance matrix, related local vertex invariants and topological indices[J]. Journal of Mathematical Chemistry, 1993, 12, 309- 31. doi: 10.1007/BF01164642
3	Plavüić D , Nikolić S , Trinajstić N , et al. On the Harary index for the characterization of chemical graphs[J]. Journal of Mathematical Chemistry, 1993, 12, 235- 250. doi: 10.1007/BF01164638
4	Liu R F , Du X , Jia H C . Some observations on Harary index and traceable graphs[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2017, 77, 195- 208.
5	Yu G D, Yu T, Shu A X, et al. Some sufficient conditions on pancyclic graphs[J]. 2018, arXiv: 1809.09897v1.
6	Indulal G . Sharp bounds on the distance spectral radius and the distance energy of graphs[J]. Linear Algebra and Its Applications, 2009, 430, 106- 113. doi: 10.1016/j.laa.2008.07.005

G	$ \rho^{\mathcal{D}}(G) $	$ n+3-\frac{14}{n} $
$ K_{5}\vee 6K_{1} $	13.245	12.727
$ K_{3}\vee (K_{2}+3K_{1}) $	9.594 7	9.25
$ K_{3}\vee (K_{1, 4}+K_{1}) $	10.834 1	10.444
$ K_{3}\vee(K_{1, 3}+K_{2}) $	10.767 2	10.444
$ (K_{2}\vee 2K_{1})\vee 5K_{1} $	10.762 4	10.444
$ K_{4}\vee 5K_{1} $	10.632 5	10.444
$ K_{1, 2}\vee 4K_{1} $	8.273 6	8
$ K_{2}\vee(K_{1, 3}+K_{1}) $	8	8
$ K_{3}\vee4K_{1} $	8	8

	$ {\rho}^{\star}(\overline{G}) $	$ \frac{5n^{2}-23n+28}{n(n-1)} $
$ K_{5}\vee 6K_{1} $	5	3.454 6
$ K_{3}\vee (K_{2}+3K_{1}) $	4.066 3	2.928 6
$ K_{3}\vee (K_{1, 4}+K_{1}) $	4.411 5	3.138 9
$ K_{3}\vee(K_{1, 3}+K_{2}) $	4.545 5	3.138 9
$ (K_{2}\vee 2K_{1})\vee 5K_{1} $	4	3.138 9
$ K_{4}\vee 5K_{1} $	4	3.138 9
$ K_{1, 2}\vee 4K_{1} $	3	2.667
$ K_{2}\vee(K_{1, 3}+K_{1}) $	3.457 5	2.667
$ K_{3}\vee4K_{1} $	3	2.667

[1]	张杰, 姬燕. 单圈图的Steiner Wiener指数的极值问题[J]. 运筹学学报, 2023, 27(3): 178-184.
[2]	邢抱花, 蔡改香. 固定直径的树的Wiener指数[J]. 运筹学学报, 2011, 15(4): 36-44.

基于Wiener指数和Harary指数的泛圈图的充分条件

Sufficient conditions on Wiener index and Harary index for pancyclic graphs

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