Skip to main content
SpringerLink
Log in

On sufficient topological indices conditions for properties of graphs

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

In this paper, we present sufficient conditions on eccentric connectivity index, eccentric distance sum and connective eccentricity index for graphs to be k-hamiltonian, k-edge-hamiltonian or k-path-coverable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bondy JA, Chvátal V (1976) A method in graph theory. Discrete Math 15:111–135

    Article  MathSciNet  Google Scholar 

  • Bondy JA, Murty USR (2008) Graph Theory, Grad Texts in Math, vol 244. Springer, New York

    Google Scholar 

  • Chvátal V (1972) On Hamiltons ideals. J Combin Theory Ser B 12:163–168

    Article  MathSciNet  Google Scholar 

  • Dobrynin AA, Entringer R, Gutman I (2001) Wiener index of trees: theory and applications. Acta Appl Math 66:211–249

    Article  MathSciNet  Google Scholar 

  • Dobrynin AA, Gutman I, Klavžar S, Žigert P (2002) Wiener index of hexagonal systems. Acta Appl Math 72:247–294

    Article  MathSciNet  Google Scholar 

  • Feng LH, Zhu XM, Liu WJ (2017) Wiener index, Harary index and graph properties. Discrete Appl Math 223:72–83

    Article  MathSciNet  Google Scholar 

  • Gupta S, Singh M, Madan AK (2000) Connective eccentricity index: a novel topological descriptor for predicting biological activity. J Mol Graph Model 18:18–25

    Article  Google Scholar 

  • Gupta S, Singh M, Madan AK (2002) Eccentric distance sum: A novel graph invariant for predicting biological and physical properties. J Math Anal Appl 275:386–401

    Article  MathSciNet  Google Scholar 

  • Hua HB, Ning B (2017) Wiener index, Harary index and Hamiltonicity of graphs. MATCH Commun Math Comput Chem 78:153–162

    MathSciNet  Google Scholar 

  • Hua HB, Wang ML (2013) On Harary index and traceable graphs. MATCH Commun Math Comput Chem 70:297–300

    MathSciNet  MATH  Google Scholar 

  • Ilić A, Yu GH, Feng LH (2011) On the eccentric distance sum of graphs. J Math Anal Appl 381:590–600

    Article  MathSciNet  Google Scholar 

  • Kronk HV (1969) A note on \(k\)-path hamiltonian graphs. J Combin Theory 7:104–106

    Article  MathSciNet  Google Scholar 

  • Kuang MJ, Huang GH, Deng HY (2016) Some sufficient conditions for Hamiltonian property in terms of Wiener-type invariants. Proc Indian Acad Sci (Math Sci) 126:1–9

    Article  MathSciNet  Google Scholar 

  • Lesniak L (1976) On \(n\)-hamiltonian graphs. Discrete Math 14:165–169

    Article  MathSciNet  Google Scholar 

  • Liu RF, Du X, Jia HC (2017) Some observations on Harary index and traceable graphs. MATCH Commun Math Comput Chem 77:195–208

    MathSciNet  Google Scholar 

  • Liu RF, Du X, Jia HC (2016) Wiener index on traceable and Hamiltonian graphs. Bull Aust Math Soc 94:362–372

    Article  MathSciNet  Google Scholar 

  • Plesník J (1984) On the sum of all distances in a graph or diagraph. J Graph Theory 8:1–21

    Article  MathSciNet  Google Scholar 

  • Sharma V, Goswami R, Madan AK (1997) Eccentric connectivity index: a novel highly discriminating topological descriptor for structrue property and structure activity studies. J Chem Inf Comput Sci 37:273–282

    Article  Google Scholar 

  • Wiener H (1947) Structural determination of paraffin boiling points. J Am Chem Soc 69:17–20

    Article  Google Scholar 

  • Yang LH (2013) Wiener index and traceable graphs. Bull Aust Math Soc 88:380–383

    Article  MathSciNet  Google Scholar 

  • Yu GH, Feng LH, Ilić A (2011) On the eccentric distance sum of trees and unicyclic graphs. J Math Anal Appl 375:99–107

    Article  MathSciNet  Google Scholar 

  • Yu GH, Qu H, Tang L, Feng LH (2014) On the connecive eccentricity index of trees and unicyclic graphs with given diameter. J Math Aanl Appl 420:1776–1786

    Article  Google Scholar 

  • Zhou B, Du Z (2010) On eccentric connectivity incex. MATCH Commun Math Comput Chem 63:181–198

    MathSciNet  MATH  Google Scholar 

  • Zhou QN, Wang LG, Lu Y (2018a) Wiener index and Harary index on Hamilton-connected graphs with large minimum degree. Discrete Appl Math 247:180–185

    Article  MathSciNet  Google Scholar 

  • Zhou QN, Wang LG, Lu Y (2019) Wiener-type invariants and Hamiltonian properties of graphs. Filomat 33:4045–4058

    Article  MathSciNet  Google Scholar 

  • Zhou QN, Wang LG, Lu Y (2018b) Wiener-type invariants on graph properties. Filomat 32:489–502

    Article  MathSciNet  Google Scholar 

  • Zhu XM, Feng LH, Liu MM, Liu WJ, Hu YQ (2017) Some topological indices and graph properties. Trans Comb 6:51–65

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to express their sincere gratitude to the anonymous referees for the valuable comments and suggestions, which improved the presentation of this paper.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, China

    Yong Lu & Qiannan Zhou

Authors
  1. Yong Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiannan Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong Lu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work is supported by the National Natural Science Foundations of China (No. 11901253), the Natural Science Foundation for Colleges and Universities in Jiangsu Province of China (No. 19KJB110009), and the Science Foundation of Jiangsu Normal University (No. 18XLRX021).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, Y., Zhou, Q. On sufficient topological indices conditions for properties of graphs. J Comb Optim 41, 487–503 (2021). https://doi.org/10.1007/s10878-021-00700-w

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-021-00700-w

Keywords

Mathematics Subject Classification

Search

Navigation