On stress sum eigenvalues and stress sum energy of graphs
Résumé
In this article, we introduce the stress sum matrix $SSM(G)$ for a graph $G$, which is related to the stress sum index. We explore the properties of this matrix, establish bounds on its eigenvalues, and define the stress sum energy $\mathcal{E}_{SS}(G)$ as the sum of the absolute eigenvalues. Additionally, we discuss its potential chemical relevance by comparing $\mathcal{E}_{SS}(G)$ with the $\pi$-electron energy of polyaromatic hydrocarbons.
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Références
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Spectral Analysis of Arithmetic Function Signed Graphs, \emph{Glob. Stoch. Anal.}, 11(3) (2024), 50-59.
\bibitem{haa1} H. A. AlFran, P. Somashekar and P. Siva Kota Reddy, Modified Kashvi-Tosha Stress Index for Graphs, \emph{Glob. Stoch. Anal.}, 12(1) (2025), 10-20.
\bibitem{brou} A. E. Brouwer and W. H. Haemers, \emph{Spectra of Graphs-Monograph}, Springer, 2011.
\bibitem{bdr} K. Bhargava, N. N. Dattatreya, and R. Rajendra, On stress of a vertex in a graph, \emph{Palest. J. Math.}, 12(3) (2023), 15–25.
\bibitem{cvet} D. M. Cvetkovi\'{c}, M. Doob and H. Sachs, \emph{Spectra of Graphs}, Academic Press, 1979.
\bibitem{gut1} I. Gutman, The energy of a graph,
\emph{Ber. Math.-Stat. Sekt. Forschungszent. Graz}, 103 (1978), 1-22.
\bibitem{gut2} I. Gutman, S. Z. Firoozabadi, J. A. de la Pe\~{n}a, J. Rada, On the energy of regular graphs,
\emph{MATCH Commun. Math. Comput. Chem.}, 57 (2007), 435-442
\bibitem{hara} F. Harary, \emph{Graph Theory}, Addison Wesley, Reading, Mass, 1972.
\bibitem{kir} M. Kirankumar, M. Ruby Salestina, C. N. Harshavardhana, R. Kemparaju and P. Siva Kota Reddy, On Stress Product Eigenvalues and Energy of Graphs, \emph{Glob. Stoch. Anal.}, 12(1) (2025), 111-123.
\bibitem{mah} K. B. Mahesh, R. Rajendra and P. Siva Kota Reddy, Square Root Stress Sum Index for Graphs, \emph{Proyecciones}, 40(4) (2021), 927-937.
\bibitem{rak} R. Poojary, K. Arathi Bhat, S. Arumugam and K. Manjunatha Prasad, The stress of a graph, \emph{Commun. Comb. Optim.}, 8(1) (2023), 53--65.
\bibitem{sp1} K. N. Prakasha, P. Siva kota Reddy and I. N. Cangul, Partition Laplacian Energy of a Graph, \emph{Adv. Stud. Contemp. Math., Kyungshang}, 27(4) (2017), 477-494.
\bibitem{sp2} K. N. Prakasha, P. Siva kota Reddy and I. N. Cangul, Minimum Covering Randic energy of a graph, \emph{Kyungpook Math. J.}, 57(4) (2017), 701-709.
\bibitem{sp3} K. N. Prakasha, P. Siva kota Reddy and I. N. Cangul, Sum-Connectivity Energy of Graphs, \emph{Adv.\ Math.\ Sci.\ Appl.}, 28(1) (2019), 85-98.
\bibitem{sp4} K. N. Prakasha, P. Siva Kota Reddy, I. N. Cangul and S. Purushotham, Atom-Bond-Connectivity Energy of Graphs, \emph{TWMS J. App. Eng. Math.}, 14(4) (2024), 1689-1704.
\bibitem{rsh} R. Rajendra, P. Siva Kota Reddy, C. N. Harshavardhana, Stress-Sum index of graphs, \emph{Sci. Magna}, 15(1) (2020), 94-103.
\bibitem{raj1} R. Rajendra, P. Siva Kota Reddy and I. N. Cangul, Stress indices of graphs, \emph{Adv. Stud. Contemp. Math. (Kyungshang)}, 31(2) (2021), 163-173.
\bibitem{raj2} R. Rajendra, P. Siva Kota Reddy and C. N. Harshavardhana, Tosha Index for Graphs, \emph{Proc. Jangjeon Math. Soc.}, 24(1) (2021), 141-147.
\bibitem{raj3} R. Rajendra, P. Siva Kota Reddy, K.B. Mahesh and C. N. Harshavardhana, Richness of a Vertex in a Graph, \emph{South East Asian J. Math. Math. Sci.}, 18(2) (2022), 149-160.
\bibitem{raj4} R. Rajendra, P. Siva Kota Reddy, C. N. Harshavardhana and Khaled A. A. Alloush, Squares Stress Sum Index for Graphs, \emph{Proc. Jangjeon Math. Soc.}, 26(4) (2023), 483-493.
\bibitem{raj5} R. Rajendra, P. Siva Kota Reddy and C. N. Harshavardhana, Stress-Difference Index for Graphs, \emph{Bol. Soc. Parana. Mat. (3)}, 42 (2024), 1-10.
\bibitem{ssr} R. Rajendra, P. Siva Kota Reddy and R. Kemparaju, Eigenvalues and Energy of Arithmetic Function Graph of a Finite Group \emph{Proc. Jangjeon Math. Soc.}, 27(1) (2024), 29-34.
\bibitem{Shimbel} A. Shimbel, Structural Parameters of Communication Networks, \emph{Bulletin of Mathematical Biophysics}, 15 (1953), 501-507.
\bibitem{somaa} P. Somashekar, P. Siva Kota Reddy, C. N. Harshavardhana and M. Pavithra, Cangul Stress Index for Graphs, \emph{J. Appl. Math. Inform.}, 42(6) (2024), 1379-1388.
Spectral Analysis of Arithmetic Function Signed Graphs, \emph{Glob. Stoch. Anal.}, 11(3) (2024), 50-59.
\bibitem{haa1} H. A. AlFran, P. Somashekar and P. Siva Kota Reddy, Modified Kashvi-Tosha Stress Index for Graphs, \emph{Glob. Stoch. Anal.}, 12(1) (2025), 10-20.
\bibitem{brou} A. E. Brouwer and W. H. Haemers, \emph{Spectra of Graphs-Monograph}, Springer, 2011.
\bibitem{bdr} K. Bhargava, N. N. Dattatreya, and R. Rajendra, On stress of a vertex in a graph, \emph{Palest. J. Math.}, 12(3) (2023), 15–25.
\bibitem{cvet} D. M. Cvetkovi\'{c}, M. Doob and H. Sachs, \emph{Spectra of Graphs}, Academic Press, 1979.
\bibitem{gut1} I. Gutman, The energy of a graph,
\emph{Ber. Math.-Stat. Sekt. Forschungszent. Graz}, 103 (1978), 1-22.
\bibitem{gut2} I. Gutman, S. Z. Firoozabadi, J. A. de la Pe\~{n}a, J. Rada, On the energy of regular graphs,
\emph{MATCH Commun. Math. Comput. Chem.}, 57 (2007), 435-442
\bibitem{hara} F. Harary, \emph{Graph Theory}, Addison Wesley, Reading, Mass, 1972.
\bibitem{kir} M. Kirankumar, M. Ruby Salestina, C. N. Harshavardhana, R. Kemparaju and P. Siva Kota Reddy, On Stress Product Eigenvalues and Energy of Graphs, \emph{Glob. Stoch. Anal.}, 12(1) (2025), 111-123.
\bibitem{mah} K. B. Mahesh, R. Rajendra and P. Siva Kota Reddy, Square Root Stress Sum Index for Graphs, \emph{Proyecciones}, 40(4) (2021), 927-937.
\bibitem{rak} R. Poojary, K. Arathi Bhat, S. Arumugam and K. Manjunatha Prasad, The stress of a graph, \emph{Commun. Comb. Optim.}, 8(1) (2023), 53--65.
\bibitem{sp1} K. N. Prakasha, P. Siva kota Reddy and I. N. Cangul, Partition Laplacian Energy of a Graph, \emph{Adv. Stud. Contemp. Math., Kyungshang}, 27(4) (2017), 477-494.
\bibitem{sp2} K. N. Prakasha, P. Siva kota Reddy and I. N. Cangul, Minimum Covering Randic energy of a graph, \emph{Kyungpook Math. J.}, 57(4) (2017), 701-709.
\bibitem{sp3} K. N. Prakasha, P. Siva kota Reddy and I. N. Cangul, Sum-Connectivity Energy of Graphs, \emph{Adv.\ Math.\ Sci.\ Appl.}, 28(1) (2019), 85-98.
\bibitem{sp4} K. N. Prakasha, P. Siva Kota Reddy, I. N. Cangul and S. Purushotham, Atom-Bond-Connectivity Energy of Graphs, \emph{TWMS J. App. Eng. Math.}, 14(4) (2024), 1689-1704.
\bibitem{rsh} R. Rajendra, P. Siva Kota Reddy, C. N. Harshavardhana, Stress-Sum index of graphs, \emph{Sci. Magna}, 15(1) (2020), 94-103.
\bibitem{raj1} R. Rajendra, P. Siva Kota Reddy and I. N. Cangul, Stress indices of graphs, \emph{Adv. Stud. Contemp. Math. (Kyungshang)}, 31(2) (2021), 163-173.
\bibitem{raj2} R. Rajendra, P. Siva Kota Reddy and C. N. Harshavardhana, Tosha Index for Graphs, \emph{Proc. Jangjeon Math. Soc.}, 24(1) (2021), 141-147.
\bibitem{raj3} R. Rajendra, P. Siva Kota Reddy, K.B. Mahesh and C. N. Harshavardhana, Richness of a Vertex in a Graph, \emph{South East Asian J. Math. Math. Sci.}, 18(2) (2022), 149-160.
\bibitem{raj4} R. Rajendra, P. Siva Kota Reddy, C. N. Harshavardhana and Khaled A. A. Alloush, Squares Stress Sum Index for Graphs, \emph{Proc. Jangjeon Math. Soc.}, 26(4) (2023), 483-493.
\bibitem{raj5} R. Rajendra, P. Siva Kota Reddy and C. N. Harshavardhana, Stress-Difference Index for Graphs, \emph{Bol. Soc. Parana. Mat. (3)}, 42 (2024), 1-10.
\bibitem{ssr} R. Rajendra, P. Siva Kota Reddy and R. Kemparaju, Eigenvalues and Energy of Arithmetic Function Graph of a Finite Group \emph{Proc. Jangjeon Math. Soc.}, 27(1) (2024), 29-34.
\bibitem{Shimbel} A. Shimbel, Structural Parameters of Communication Networks, \emph{Bulletin of Mathematical Biophysics}, 15 (1953), 501-507.
\bibitem{somaa} P. Somashekar, P. Siva Kota Reddy, C. N. Harshavardhana and M. Pavithra, Cangul Stress Index for Graphs, \emph{J. Appl. Math. Inform.}, 42(6) (2024), 1379-1388.
Publiée
2025-04-15
Numéro
Rubrique
Research Articles
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