中文

Operations Research Transactions >

2023 , Vol. 27 >Issue 3: 169 - 177

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2023.03.014

Sufficient conditions on Wiener index and Harary index for pancyclic graphs

Expand
  • 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 date: 2020-04-04

  Online published: 2023-09-14

Fold

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

Cite this article

Huicai JIA, Hongye SONG . Sufficient conditions on Wiener index and Harary index for pancyclic graphs[J]. Operations Research Transactions, 2023 , 27(3) : 169 -177 . DOI: 10.15960/j.cnki.issn.1007-6093.2023.03.014

References

1 Wiener H . Structural determination of paraffin boiling points[J]. Journal of the American Chemical Society, 1947, 69, 17- 20.
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.
3 Plavüi? D , Nikoli? S , Trinajsti? N , et al. On the Harary index for the characterization of chemical graphs[J]. Journal of Mathematical Chemistry, 1993, 12, 235- 250.
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.
Options
Outlines

/

〈 〉