Research Article

Degree distance and Gutman index of two graph products

Volume: 7 Number: 2 May 7, 2020
  • Shaban Sedghı *
  • Nabi Shobe
EN

Degree distance and Gutman index of two graph products

Abstract

The degree distance was introduced by Dobrynin, Kochetova and Gutman as a weighted version of the Wiener index. In this paper, we investigate the degree distance and Gutman index of complete, and strong product graphs by using the adjacency and distance matrices of a graph.

Keywords

References

  1. [1] A. Alwardi, B. Arsic, I. Gutman, N. D. Soner, The common neighborhood graph and its energy, Iran. J. Math. Sci. Inf. 7 (2012) 1–8.
  2. [2] J. A. Bondy, U. S. R. Murty, Graph theory, Springer, New York, 2008.
  3. [3] A. S. Bonifácio, R. R. Rosa, I. Gutman, N. M. M. de Abreu, Complete common neighborhood graphs, Proceedings of Congreso Latino-Iberoamericano de Investigaci on Operativa and Simposio Brasileiro de Pesquisa Operacional (2012) 4026–4032.
  4. [4] S. Chen, Cacti with the smallest, second smallest, and third smallest Gutman index, J. Combin. Optim. 31(1) (2016) 327–332.
  5. [5] S. Chen, Z. Guo, A lower bound on the degree distance in a tree, Int. J. Contemp. Math. Sci. 5(13) (2010) 649–652.
  6. [6] P. Dankelmann, I. Gutman, S. Mukwembi, H.C. Swart, On the degree distance of a graph, Discrete Appl. Math. 157(13) (2009) 2773–2777.
  7. [7] P. Dankelmann, I. Gutman, S. Mukwembi, H. C. Swart, The edge–Wiener index of a graph, Discrete Math. 309 (2009) 3452–457.
  8. [8] A. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: Theory and applications, Acta Appl. Math. 66 (2001) 211–249.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Shaban Sedghı * This is me
Iran

Nabi Shobe This is me
Iran

Publication Date

May 7, 2020

Submission Date

August 10, 2017

Acceptance Date

August 15, 2019

Published in Issue

Year 2020 Volume: 7 Number: 2

APA
Sedghı, S., & Shobe, N. (2020). Degree distance and Gutman index of two graph products. Journal of Algebra Combinatorics Discrete Structures and Applications, 7(2), 121-140. https://doi.org/10.13069/jacodesmath.729422
AMA
1.Sedghı S, Shobe N. Degree distance and Gutman index of two graph products. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020;7(2):121-140. doi:10.13069/jacodesmath.729422
Chicago
Sedghı, Shaban, and Nabi Shobe. 2020. “Degree Distance and Gutman Index of Two Graph Products”. Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2): 121-40. https://doi.org/10.13069/jacodesmath.729422.
EndNote
Sedghı S, Shobe N (May 1, 2020) Degree distance and Gutman index of two graph products. Journal of Algebra Combinatorics Discrete Structures and Applications 7 2 121–140.
IEEE
[1]S. Sedghı and N. Shobe, “Degree distance and Gutman index of two graph products”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 7, no. 2, pp. 121–140, May 2020, doi: 10.13069/jacodesmath.729422.
ISNAD
Sedghı, Shaban - Shobe, Nabi. “Degree Distance and Gutman Index of Two Graph Products”. Journal of Algebra Combinatorics Discrete Structures and Applications 7/2 (May 1, 2020): 121-140. https://doi.org/10.13069/jacodesmath.729422.
JAMA
1.Sedghı S, Shobe N. Degree distance and Gutman index of two graph products. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020;7:121–140.
MLA
Sedghı, Shaban, and Nabi Shobe. “Degree Distance and Gutman Index of Two Graph Products”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 7, no. 2, May 2020, pp. 121-40, doi:10.13069/jacodesmath.729422.
Vancouver
1.Shaban Sedghı, Nabi Shobe. Degree distance and Gutman index of two graph products. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020 May 1;7(2):121-40. doi:10.13069/jacodesmath.729422

Cited By

General degree distance of graphs

Journal of Algebra Combinatorics Discrete Structures and Applications

https://doi.org/10.13069/jacodesmath.935980