IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i1p83-d197683.html
   My bibliography  Save this article

The Extremal Cacti on Multiplicative Degree-Kirchhoff Index

Author

Listed:
  • Fangguo He

    (College of Mathematics and Physics, Huanggang Normal University, Huanggang 438000, China)

  • Zhongxun Zhu

    (College of Mathematics and Statistics, South Central University for Nationalities, Wuhan 430074, China)

Abstract

For a graph G , the resistance distance r G ( x , y ) is defined to be the effective resistance between vertices x and y , the multiplicative degree-Kirchhoff index R ∗ ( G ) = ∑ { x , y } ⊂ V ( G ) d G ( x ) d G ( y ) r G ( x , y ) , where d G ( x ) is the degree of vertex x , and V ( G ) denotes the vertex set of G . L. Feng et al. obtained the element in C a c t ( n ; t ) with first-minimum multiplicative degree-Kirchhoff index. In this paper, we first give some transformations on R ∗ ( G ) , and then, by these transformations, the second-minimum multiplicative degree-Kirchhoff index and the corresponding extremal graph are determined, respectively.

Suggested Citation

  • Fangguo He & Zhongxun Zhu, 2019. "The Extremal Cacti on Multiplicative Degree-Kirchhoff Index," Mathematics, MDPI, vol. 7(1), pages 1-12, January.
  • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:83-:d:197683
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/1/83/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/7/1/83/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:83-:d:197683. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.