Kepler Stress Exponential for Graphs

M. Kirankumar; K. R. Karthik; Pavithra M; Puttaswamy

doi:10.5269/bspm.76746

M. Kirankumar Vidyavardhaka College of Engineering, Mysuru
K. R. Karthik P.E.S College of Engineering, Mandya-571 401, INDIA.
Pavithra M Karnataka State Open University
Puttaswamy P.E.S College of Engineering, Mandya-571 401, INDIA.

Resumo

In 1953, Alfonso Shimbel introduced the concept of vertex stress in a graph. The stress of a vertex in a graph is the number of shortest paths passing through it. This paper describes the Kepler stress exponential $KS(G,x)$ of graphs and presents findings, including a characterization of graphs with non-zero constant vertex stress polynomials. Similarly, we established the importance of the Kepler stress exponential in predicting the physicochemical properties of butane derivatives.

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Biografia do Autor

M. Kirankumar, Vidyavardhaka College of Engineering, Mysuru

Assistant Professor, Department of Mathematics

K. R. Karthik, P.E.S College of Engineering, Mandya-571 401, INDIA.

Assistant Professor, Department of Mathematics

Puttaswamy, P.E.S College of Engineering, Mandya-571 401, INDIA.

Professor and Head, Department of Mathematics

Referências

AlFran, H. A., Somashekar, P. and Siva Kota Reddy, P., Modified Kashvi-Tosha Stress Index for Graphs, Glob. Stoch. Anal., 12(1), 10-20, (2025).

Almkvist, G., and Berndt, B. C., Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π , and the Ladies Diary, Am. Math. Mon., 95(7), 585-608, (1988).

Bhargava, K., Dattatreya, N. N. and Rajendra, R., On stress of a vertex in a graph, Palest. J. Math., 12(3), 15–25, (2023).

Gutman, I., Furtula, B. and Oz, M. S. Geometric approach to vertex-degree-based topological indices–Elliptic Sombor index, theory and application, Int. J. Quantum Chem., 124(2), Article ID: e27346, (2024).

Harary, F., Graph Theory, Addison Wesley, Reading, Mass, (1972).

Indhumathy, M., Arumugam, S., Baths, Veeky and Singh, Tarkeshwar, Graph theoretic concepts in the study of biological networks, Applied Analysis in Biological and Physical Sciences, Springer Proceedings in Mathematics & Statistics, 186, 187-200, (2016).

Kulli, V. R., Kepler Banhatti and Modified Kepler Banhatti indices, International Journal of Mathematics and Computer Research, 12(6), 4310-4314, (2024).

Mahesh, K. B., Rajendra, R. and Siva Kota Reddy, P., Square Root Stress Sum Index for Graphs, Proyecciones, 40(4), 927-937, (2021).

Mangala Gowramma, H., Siva Kota Reddy, P., Kim, T. and Rajendra, R., Taekyun Kim Stress Power α-Index, Bol. Soc. Parana. Mat. (3), 43, Article Id: 72273, 10 Pages, (2025).

Mangala Gowramma, H., Siva Kota Reddy, P., Kim, T. and Rajendra, R., Taekyun Kim α-Index of Graphs, Bol. Soc. Parana. Mat. (3), 43, Article Id: 72275, 10 Pages, (2025).

Mangala Gowramma, H., Siva Kota Reddy, P., Hemavathi, P. S., Pavithra, M. and Rajendra, R., Total Stress as a Topological Index, Proc. Jangjeon Math. Soc., 28(2), 181-188, (2025).

Nalina, C., Siva Kota Reddy, P., Kirankumar, M. and Pavithra, M., On Stress Sum Eigenvalues and Stress Sum Energy of Graphs, Bol. Soc. Parana. Mat. (3), 43, Article Id: 75954, 15 Pages, (2025).

Pinto, R. M., Rajendra, R., Siva Kota Reddy, P. and Cangul, I. N., A QSPR Analysis for Physical Properties of Lower Alkanes Involving Peripheral Wiener Index, Montes Taurus J. Pure Appl. Math., 4(2), 81–85, (2022).

Rai, P. S., Rajendra, R. and Siva Kota Reddy, P., Vertex Stress Polynomial of a Graph, Bol. Soc. Parana. Mat. (3), 43, Article Id: 68311, 6 Pages, (2025).

Rajendra, R., Mahesh, K. B. and Siva Kota Reddy, P., Mahesh Inverse Tension Index for Graphs, Adv. Math., Sci. J., 9(12), 10163-10170, (2020).

Rajendra, R., Siva Kota Reddy, P. and Cangul, I. N., Stress indices of graphs, Adv. Stud. Contemp. Math. (Kyungshang), 31(2), 163-173, (2021).

Rajendra, R., Siva Kota Reddy, P. and Harshavardhana, C. N., Tosha Index for Graphs, Proc. Jangjeon Math. Soc., 24(1), 141-147, (2021).

Rajendra, R., Siva Kota Reddy, P., Harshavardhana, C. N., and Alloush, Khaled A. A., Squares Stress Sum Index for Graphs, Proc. Jangjeon Math. Soc., 26(4), 483-493, (2023).

Rajendra, R., Siva Kota Reddy, P. and Harshavardhana, C. N., Stress-Difference Index for Graphs, Bol. Soc. Parana. Mat. (3), 42, 1-10, (2024).

Shannon, P., Markiel, A., Ozier, O., Baliga, N. S., Wang, J. T., Ramage, D., Amin, N., Schwikowski, B., and Idekar, T., Cytoscape: a software environment for integrated models of biomolecular interaction networks, Genome Res., 13(11), 2498–2504, (