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

Operations Research Transactions ›› 2023, Vol. 27 ›› Issue (3): 169-177.doi: 10.15960/j.cnki.issn.1007-6093.2023.03.014

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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

Abstract

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

CLC Number:

O221

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

Figures/Tables 2

References 6

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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]	ZHANG Jie, JI Yan. Extremal problems for Steiner Wiener index of unicyclic graphs [J]. Operations Research Transactions, 2023, 27(3): 178-184.
[2]	CAI Gaixiang, XING Baohua, YU Guidong. The Harary index of tricyclic graphs [J]. Operations Research Transactions, 2015, 19(2): 45-53.
[3]	XING Bao-Hua, Cai-Gai-Xiang. The Wiener Index of Trees with Prescribed Diameter [J]. Operations Research Transactions, 2011, 15(4): 36-44.

Sufficient conditions on Wiener index and Harary index for pancyclic graphs

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