Skip to main content
SpringerLink
Log in

On the maximal eccentric connectivity indices of graphs

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

For a connected simple graph G, the eccentricity ec(v) of a vertex v in G is the distance from v to a vertex farthest from v, and d(v) denotes the degree of a vertex v. The eccentric connectivity index of G, denoted by ξ c(G), is defined as Σ v∈V(G) d(v)ec(v). In this paper, we will determine the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges(n ≤ m ≤ n+4), and propose a conjecture on the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges (m ≥ n +5).

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. A R Ashrafi, M Saheli, M Ghorbani. The eccentric connectivity index of nanotubes and nanotori, J Comput Appl Math, 2011, 235: 4561–4566.

    Article  MathSciNet  MATH  Google Scholar 

  2. S Gupta, M Singh, A K Madan. Application of graph theory: Relationship of eccentric connectivity index and Wiener’s index with anti-inflammatory activity, J Math Anal Appl, 2002, 266: 259–268.

    Article  MathSciNet  MATH  Google Scholar 

  3. A Ilić, I Gutman. Eccentric connectivity index of chemical trees, MATCH Commun Math Comput Chem, 2011, 65: 731–744.

    MathSciNet  MATH  Google Scholar 

  4. M J Morgan, S Mukwembi, H C Swart. On the eccentric connectivity index of a garph, Discrete Math, 2011, 311: 1299–1234.

    Article  MathSciNet  Google Scholar 

  5. V Sharma, R Goswami, A K Madan. Eccentric connectivity index: A novel highly discriminating topological descriptor for structure-property and structure-activity studies, J Chem Inf Comput Sci, 1997, 37: 273–282.

    Article  Google Scholar 

  6. B Zhou, Z Du. On eccentric connectivity index, MATCH Commun Math Comput Chem, 2010, 63: 181–198.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, South China Normal University, Guangzhou, 510631, China

    Jian-bin Zhang & Bo Zhou

  2. Department of Mathematics, Huizhou University, Huizhou, 516007, China

    Zhong-zhu Liu

Authors
  1. Jian-bin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhong-zhu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bo Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian-bin Zhang.

Additional information

Supported by China Postdoctoral Science Foundation (2012M520815 and 2013T60411), and the National Natural Science Foundation of China (11001089).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Jb., Liu, Zz. & Zhou, B. On the maximal eccentric connectivity indices of graphs. Appl. Math. J. Chin. Univ. 29, 374–378 (2014). https://doi.org/10.1007/s11766-014-3023-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-014-3023-7

MR Subject Classification

Keywords

Search

Navigation