On Cangul stress energy of graphs

P. Somashekar; Dr Siva Kota Reddy Polaepalli; M. Kirankumar; M. Pavithra; Howida Adel  AlFran

doi:10.5269/bspm.76033

P. Somashekar Maharani's Science College for Women (Autonomous)
Dr Siva Kota Reddy Polaepalli JSS Science and Technology University http://orcid.org/0000-0003-4033-8148
M. Kirankumar Vidyavardhaka College of Engineering, Mysuru
M. Pavithra Karnataka State Open University, Mysuru
Howida Adel AlFran

Resumo

In this article, we introduce the Cangul stress matrix \( CSM(G) \) for a connected graph \( G \), which is associated with the Cangul stress index. We investigate the properties of this matrix, establish bounds on its eigenvalues, and define the Cangul stress energy \( E_{CSM}(G) \) as the sum of the absolute values of the eigenvalues. Furthermore, we examine its potential relevance in chemistry by comparing \( E_{CSM}(G) \) with the \( \pi \)-electron energy of benzene derivatives.

Downloads

Não há dados estatísticos.

Biografia do Autor

P. Somashekar, Maharani's Science College for Women (Autonomous)

Associate Professor, Department of Mathematics

Dr Siva Kota Reddy Polaepalli, JSS Science and Technology University

Professor, Departmnet of Mathematics, JSS Science and Technology, Mysuru-570 006, India

M. Kirankumar, Vidyavardhaka College of Engineering, Mysuru

Assistant Professor, Department of Mathematics

M. Pavithra, Karnataka State Open University, Mysuru

Associate Professor, Department of Studies in Mathematics

Referências

AlFran, H. A., Rajendra, R., Siva Kota Reddy, P., Kemparaju, R. and Altoum, Sami H., Spectral Analysis of Arithmetic Function Signed Graphs, Glob. Stoch. Anal., 11(3), 50-59, (2024).

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).

Brouwer, A. E. and Haemers, W. H., Spectra of Graphs-Monograph, Springer, (2011).

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

Cvetkovc, D. M., Doob, M. and Sachs, H., Spectra of Graphs, Academic Press, (1979).

Gutman, I., The energy of a graph, Ber. Math.-Stat. Sekt. Forschungszent. Graz, 103, 1-22, (1978).

Gutman, I., Firoozabadi, S. Z., de la Pe˜na, J. A. and Rada, J., On the energy of regular graphs, MATCH Commun. Math. Comput. Chem., 57, 435-442, (2007).

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

Hemavathi, P. S., Mangala Gowramma, H., Kirankumar, M., Pavithra, M. and Siva Kota Reddy, P., On Minimum Stress Energy of Graphs, J. Appl. Math. Inform., 43(2), 543-557, (2025).

Kirankumar, M., Ruby Salestina, M., Harshavardhana, C. N., Kemparaju, R. and Siva Kota Reddy, P., On Stress Product Eigenvalues and Energy of Graphs, Glob. Stoch. Anal., 12(1), 111-123, (2025).

Kirankumar, M., Harshavardhana, C. N., Ruby Salestina, M., Pavithra, M. and Siva Kota Reddy, P., On Sombor Stress Energy of Graphs, J. Appl. Math. Inform., 43(2), 475-490, (2025).

Lokesha, V., Shanthakumari, Y. and Siva Kota Reddy, P., Skew-Zagreb Energy of Directed Graphs, Proc. Jangjeon Math. Soc., 23(4), 557-568, (2020).

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).

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).

Poojary, R., Arathi Bhat, K., Arumugam, S. and Manjunatha Prasad, K., The stress of a graph, Commun. Comb. Optim., 8(1), 53-65, (2023).

Prakasha, K. N., Siva kota Reddy, P. and Cangul, I. N., Partition Laplacian Energy of a Graph, Adv. Stud. Contemp. Math., Kyungshang, 27(4), 477-494, (2017).

Prakasha, K. N., Siva Kota Reddy, P. and Cangul, I. N., Minimum Covering Randic energy of a graph, Kyungpook Math. J., 57(4), 701-709, (2017).

Prakasha, K. N., Siva Kota Reddy, P. and Cangul, I. N., Sum-Connectivity Energy of Graphs, Adv. Math. Sci. Appl., 28(1), 85-98, (2019).

Prakasha, K. N., Siva kota Reddy, P., Cangul, I. N. and Purushotham, S., Atom-Bond-Connectivity Energy of Graphs, TWMS J. App. Eng. Math., 14(4), 1689-1704, (2024).

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., Siva Kota Reddy, P. and Harshavardhana, C. N., Stress-Sum index of graphs, Sci. Magna, 15(1), 94-103, (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., Mahesh, K.B. and Harshavardhana, C. N., Richness of a Vertex in a Graph, South East Asian J. Math. Math. Sci., 18(2), 149-160, (2022).

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).

Rajendra, R., Siva Kota Reddy, P. and Kemparaju, R., Eigenvalues and Energy of Arithmetic Function Graph of a Finite Group, Proc. Jangjeon Math. Soc., 27(1), 29-34, (2024).

Shimbel, A., Structural Parameters of Communication Networks, Bulletin of Mathematical Biophysics, 15, 501-507, (1953).

Somashekar, P., Siva Kota Reddy, P., Harshavardhana, C. N. and Pavithra, M., Cangul Stress Index for Graphs, J. Appl. Math. Inform., 42(6), 1379-1388, (2024).

Somashekar, P. and Siva Kota Reddy, P., Kashvi-Tosha Stress Index for Graphs, Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms, 32, 137-148, (2025).

Sureshkumar, S., Mangala Gowramma, H., Kirankumar, M., Pavithra, M. and Siva Kota Reddy, P., On Maximum Stress Energy of Graphs, Glob. Stoch. Anal., 12(2), 56-69, (2025).