Square root stress-sum index for graphs

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-4362

Keywords:

Stress of a vertex, Geodesic, Topological index

Abstract

The stress of a vertex is a node centrality index, which has been introduced by Shimbel (1953). The stress of a vertex in a graph is the number of geodesics (shortest paths) passing through it. In this  paper, we introduce a new topological index for graphs called square root stress sum index using stresses of vertices. Further, we establish some inequalities, prove some results and compute stress-sum index for some standard graphs.

Author Biographies

R. Rajendra, Mangalore University.

Dept. of Mathematics.

P. Siva Kota Reddy, JSS Science and Technology University.

Sri Jayachamarajendra College of Engineering, Dept. of Mathematics.

References

K. Bhargava, N.N. Dattatreya, and R. Rajendra, “On stress of a vertex in a graph”, Palestine journal of mathematics, accepted for publication.

K. C. Das, I. Gutman, I. Milovanović, E. Milovanović, and B. Furtula, “Degree-based energies of graphs”, Linear algebra and its applications, vol. 554, pp. 185-204, 2018. https://doi.org/10.1016/j.laa.2018.05.027

F. Harary, Graph theory. Reading, MA: Addison Wesley, 1972.

M. Indhumathy, S. Arumugam, V. Baths, and T. Singh, “Graph theoretic concepts in the study of biological networks”, in Applied analysis in biological and physical sciences, J. Cushing, M. Saleem, H. Srivastava, M. Khan, and M. Merajuddin, Eds. New Delhi: Springer, 2016, pp. 187–200. https://doi.org/10.1007/978-81-322-3640-5_11

P. Shannon, A. Markiel, O. Ozier, N.S. Baliga, J.T. Wang, D. Ramage, N. Amin, B. Schwikowski, and T. Idekar, “Cytoscape: a software environment for integrated models of biomolecular interaction networks”, Genome research, vol. 13, no. 11, pp. 2498-2504, 2003. https://doi.org/10.1101/gr.1239303

A. Shimbel, “Structural parameters of communication networks”, The bulletin of mathematical biophysics, vol. 15, pp. 501-507, 1953. https://doi.org/10.1007/BF02476438

Published

2021-04-28 — Updated on 2021-07-26

How to Cite

[1]
K. B. Mahesh, R. Rajendra, and P. S. K. . Reddy, “Square root stress-sum index for graphs”, Proyecciones (Antofagasta, On line), vol. 40, no. 4, pp. 927-936, Jul. 2021.

Issue

Section

Artículos

Most read articles by the same author(s)