Kirchhoff index and degree Kirchhoff index of complete multipartite graphs

Authors

Ravindra B. Bapat, Indian Statistical Institute (Delhi Centre)
Masoud Karimi, Anhui University
Jia Bao Liu, Anhui Jianzhu University

Article Type

Research Article

Publication Title

Discrete Applied Mathematics

Abstract

Given a complete multipartite graph G, we explicitly formulate the effective resistance distance between any two vertices of G, using methods from linear algebra. The Kirchhoff index and the degree Kirchhoff index are defined in terms of the effective resistance distances for any simple graph. In this paper, for G, the exact formulae for the two indices are provided. Along with these results, we obtain the optimal Kirchhoff index and the optimal degree Kirchhoff index.

First Page

41

Last Page

49

DOI

10.1016/j.dam.2017.07.040

Publication Date

12-11-2017

Comments

Open Access, Bronze

Recommended Citation

Bapat, Ravindra B.; Karimi, Masoud; and Liu, Jia Bao, "Kirchhoff index and degree Kirchhoff index of complete multipartite graphs" (2017). Journal Articles. 2302.
https://digitalcommons.isical.ac.in/journal-articles/2302