Taekyun Kim Stress Power $\alpha$-Index
Resumo
We introduce a novel topological index for graphs namely, Taekyun Kim stress power $\alpha$-index, which involves powers of stresses of nodes, where $\alpha$ is a non-negative number. We compute this index for various common graphs, prove some results, and construct some inequalities. Further, we analyze the correlation between Taekyun Kim stress power $\alpha$-index of chemical structures (molecular graphs) and physical properties of lower alkanes.
Downloads
Não há dados estatísticos.
Referências
\bibitem{bdr} K. Bhargava, N. N. Dattatreya and R. Rajendra, On stress of a node in a graph, \emph{Palest. J. Math.}, 12(3) (2023), 15–25.
\bibitem{gut1} I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $\phi$-electron energy of alternant hydrocarbons, \emph{Chemical Physics Letters}, 17(4) (1972), 535-538.
\bibitem{gut2} I. Gutman, B. Ruščić, N. Trinajstić and C. F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes, \emph{J. Chem. Phys.}, 62(9) (1975), 3399–3405.
\bibitem{gut4} I. Gutman and K. C. Das, The first Zagreb index 30 years after, \emph{MATCH Commun. Math. Comput. Chem.}, 50 (2004), 83-92.
\bibitem{hara} F. Harary, \emph{Graph Theory}, Addison Wesley, Reading, Mass, 1972.
\bibitem{harsha} C. N. Harshavardhana, R. Rajendra, P. Siva Kota Reddy and Khaled A. A. Alloush, A QSPR Analysis for Stress-Sum Index, \emph{International J. Math. Combin.}, 4 (2022), 60-65.
\bibitem{indu2} M. Indhumathy, S. Arumugam, V. Baths and T. Singh, Graph theoretic concepts in the study of biological networks, \emph{Springer Proc. Math. Stat.}, 186 (2016), 187-200.
\bibitem{Needham} D. E. Needham, I. C. Wei and P. G. Seybold, Molecular modeling of the physical properties of alkanes, \emph{Journal of the American Chemical Society}, 110(13) (1988), 4186–4194.
\bibitem{Raksha1} 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{Raksha2} R. Poojary, K. Arathi Bhat, S. Arumugam and K. Manjunatha Prasad, Stress of a graph and its computation, \emph{AKCE Int. J. Graphs Comb.}, 20(2) (2023), 200-208.
\bibitem{raj-first-stress} 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{raj-QSPR-first-stress} R. Rajendra, P. Siva Kota Reddy, I. N. Cangul and Khaled A. A. Alloush, A QSPR Analysis for Physical Properties of Lower Alkanes using First Stress Index, \emph{European Chemical Bulletin}, 12(10) (2023), 5810-5814.
\bibitem{Raj-StressSum} R. Rajendra, P. Siva Kota Reddy and C. N. Harshavardhana, Stress-Sum Index for Graphs, \emph{Sci. Magna}, 15(1) (2020), 94-103.
\bibitem{Raj-QSPR-T-S} R. Rajendra, P. Siva Kota Reddy, I. N. Cangul and H. M. Gowramma, Total Stress as a Topological Index, Submitted for publication.
\bibitem{Shannon} P. Shannon, A. Markiel, O. Ozier, N. S. Baliga, J. T. Wang, D. Ramage, N. Amin, B. Schwikowski and T. Ideker, Cytoscape: A Software Environment for Integrated Models of Biomolecular Interaction Networks, \emph{Genome Research}, 13(11) (2003), 2498–2504.
\bibitem{Shimbel} A. Shimbel, Structural Parameters of Communication Networks, \emph{Bulletin of Mathematical Biophysics}, 15 (1953), 501-507.
\bibitem{Wiener} H. Wiener, Structural determination of paraffin boiling points,
\emph{J. Amer. Chem. Soc.}, 69(1) (1947), 17-20.
\bibitem{HI} K. Xu, K. C. Das and N. Trinajstic, \emph{The Harary Index of a Graph}, Heidelberg, Springer, 2015.
\bibitem{Zhou} B. Zhou, Zagreb indices, \emph{MATCH Commun. Math. Comput. Chem.}, 52 (2004) 113–118.
\bibitem{gut1} I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $\phi$-electron energy of alternant hydrocarbons, \emph{Chemical Physics Letters}, 17(4) (1972), 535-538.
\bibitem{gut2} I. Gutman, B. Ruščić, N. Trinajstić and C. F. Wilcox, Graph theory and molecular orbitals. XII. Acyclic polyenes, \emph{J. Chem. Phys.}, 62(9) (1975), 3399–3405.
\bibitem{gut4} I. Gutman and K. C. Das, The first Zagreb index 30 years after, \emph{MATCH Commun. Math. Comput. Chem.}, 50 (2004), 83-92.
\bibitem{hara} F. Harary, \emph{Graph Theory}, Addison Wesley, Reading, Mass, 1972.
\bibitem{harsha} C. N. Harshavardhana, R. Rajendra, P. Siva Kota Reddy and Khaled A. A. Alloush, A QSPR Analysis for Stress-Sum Index, \emph{International J. Math. Combin.}, 4 (2022), 60-65.
\bibitem{indu2} M. Indhumathy, S. Arumugam, V. Baths and T. Singh, Graph theoretic concepts in the study of biological networks, \emph{Springer Proc. Math. Stat.}, 186 (2016), 187-200.
\bibitem{Needham} D. E. Needham, I. C. Wei and P. G. Seybold, Molecular modeling of the physical properties of alkanes, \emph{Journal of the American Chemical Society}, 110(13) (1988), 4186–4194.
\bibitem{Raksha1} 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{Raksha2} R. Poojary, K. Arathi Bhat, S. Arumugam and K. Manjunatha Prasad, Stress of a graph and its computation, \emph{AKCE Int. J. Graphs Comb.}, 20(2) (2023), 200-208.
\bibitem{raj-first-stress} 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{raj-QSPR-first-stress} R. Rajendra, P. Siva Kota Reddy, I. N. Cangul and Khaled A. A. Alloush, A QSPR Analysis for Physical Properties of Lower Alkanes using First Stress Index, \emph{European Chemical Bulletin}, 12(10) (2023), 5810-5814.
\bibitem{Raj-StressSum} R. Rajendra, P. Siva Kota Reddy and C. N. Harshavardhana, Stress-Sum Index for Graphs, \emph{Sci. Magna}, 15(1) (2020), 94-103.
\bibitem{Raj-QSPR-T-S} R. Rajendra, P. Siva Kota Reddy, I. N. Cangul and H. M. Gowramma, Total Stress as a Topological Index, Submitted for publication.
\bibitem{Shannon} P. Shannon, A. Markiel, O. Ozier, N. S. Baliga, J. T. Wang, D. Ramage, N. Amin, B. Schwikowski and T. Ideker, Cytoscape: A Software Environment for Integrated Models of Biomolecular Interaction Networks, \emph{Genome Research}, 13(11) (2003), 2498–2504.
\bibitem{Shimbel} A. Shimbel, Structural Parameters of Communication Networks, \emph{Bulletin of Mathematical Biophysics}, 15 (1953), 501-507.
\bibitem{Wiener} H. Wiener, Structural determination of paraffin boiling points,
\emph{J. Amer. Chem. Soc.}, 69(1) (1947), 17-20.
\bibitem{HI} K. Xu, K. C. Das and N. Trinajstic, \emph{The Harary Index of a Graph}, Heidelberg, Springer, 2015.
\bibitem{Zhou} B. Zhou, Zagreb indices, \emph{MATCH Commun. Math. Comput. Chem.}, 52 (2004) 113–118.
Publicado
2025-01-21
Edição
Seção
Artigos
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
