Square root stress-sum index for graphs
Keywords:Stress of a vertex, Geodesic, Topological index
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.
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
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