Taekyun Kim $\alpha$-Index of Graphs
Resumen
In this study, we introduce the Taekyun Kim $\alpha$-index, a novel topological index for graphs, where $\alpha\in \mathbb{R}$, which involves stresses and degrees of nodes. We calculate this index for a few common graphs and prove a few results. Further, a QSPR analysis is carried for Taekyun Kim $2$-index and physical properties of lower alkanes and linear regression models have been provided.
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\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{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. S. K. 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-StressSum} R. Rajendra, P. S. K. 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. S. K. 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-StressSum} R. Rajendra, P. S. K. 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
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Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática
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