Main Article Content
Abstract
In this paper, we introduce the higher-order Sombor index of a molecular graph. In addtition, we compute the second order Sombor index of some standard class of graphs and line graph of subdivision graph of 2D-lattice, nanotube and nanotorus of TUC_4C_8[p,q] and also we obtain the expressions of the second order Sombor index of the line graph of subdivision graph of tadpole graph, wheel graph, ladder graph and chain silicate network CSn. Further, we study the linear regression analysis of the second order Sombor index with the entropy, acentric factor, enthalpy of vaporization and standard enthalpy of vaporization of an octane isomers.
Keywords
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
- Akhter, S., Imran, M., Farahani, M. R. and Javaid, I., "On topological properties of hexagonal and silicate networks", Hacet. J. Math. Stat., 48(3) (2019), 711--723.
- Basavanagoud, B. Patil, S. and Deng, H., "On the second order first Zagreb index", Iranian J. Math. Chem., 8(3)(2017), 299--311.
- Basavanagoud, B., Desai, V. R. and patil, S., "(beta, alpha)- Connectivity Index of Graphs", Appl. Math. Nonlinear Sci., 2(1)(2017), 21--30.
- de Caen, D., "An upper bound on the sum of squares of degrees in a graph", Discrete Math., 185(1-3)(1998), 245--248.
- Das, K. Ch., "Sharp bounds for the sum of the squares of the degrees of a graph", Kragujev. J. Math., 25(2003), 31--49.
- Gutman, I. and Trinajstic, N., "Graph theory and molecular orbitals. Total $pi$-electron energy of alternant hydrocarbons", Chem. Phys. Lett., 17(4)(1972), 535--538.
- Gutman, I., "Geometric approach to degree-based topological indices:Sombor indices", textit{MATCH Common, Math. Comput. Chem.,} 86 (2021), 11--16.
- Kier, L. B., Hall, L. H., Murray, W. J. and Randi'{c}, M., Molecular Connectivity V: connectivity series concept applied to density, J. Pharm. Sci., 65(1976), 1226--1230.
- Kier, L. B. and Hall, L. H., "Molecular Connectivity in Chemistry and Drug Research", Academic Press, New York, 1976.
- Li, X. and Zhao, H., "Trees with the first three smallest and largest generalized topological indices", MATCH Commun. Math. Comput. Chem., 50 (2004), 57--62.
- Nikmehr, M. J. Veylaki, M. and Soleimani, N., "Some topological indices of V-phenylenic nanotube and nanotori", Optoelectron. Adv. Mater. Rapid Comm., 9(9)(2015), 1147--1149.
- Nadeema, M. F., Zafar, S. and Zahidb, Z. "On topological properties of the line graphs of subdivision graphs of certain nanostructures", Appl. Math. Comput., 273 (2016), 125--130.
- Randi'{c}, M., "Characterization of molecular branching", J. Am. Chem. Soc., 97 (1975), 6609--6615.
- Nadeem, M. F., Zafar, S. and Zahidb, Z., "On certain topological indices of the line graph of subdivision graphs", Appl. Math. Comput., 271(2015), 790--794.
- Ranjini, P. S., Lokesha, V. and Cang"{u}l, I. N., "On the Zagreb indices of the line graphs of the subdivision graphs", Appl. Math. Comput., 218}(3) (2011), 699--702.
- Ranjini, P. S., Lokesha, V., Rajan, M. A. and Raju, M. P., "On the Shultz index of the subdivision graphs", Adv. Stud. Contemp. Math., (Kyungshang) 21(3)(2011), 279--290.
- Su, G. and Xu, L., "Topological indices of the line graph of subdivision graphs and their Schur-bounds",Appl. Math. Comput., 253 (2015), 395--401.
References
Akhter, S., Imran, M., Farahani, M. R. and Javaid, I., "On topological properties of hexagonal and silicate networks", Hacet. J. Math. Stat., 48(3) (2019), 711--723.
Basavanagoud, B. Patil, S. and Deng, H., "On the second order first Zagreb index", Iranian J. Math. Chem., 8(3)(2017), 299--311.
Basavanagoud, B., Desai, V. R. and patil, S., "(beta, alpha)- Connectivity Index of Graphs", Appl. Math. Nonlinear Sci., 2(1)(2017), 21--30.
de Caen, D., "An upper bound on the sum of squares of degrees in a graph", Discrete Math., 185(1-3)(1998), 245--248.
Das, K. Ch., "Sharp bounds for the sum of the squares of the degrees of a graph", Kragujev. J. Math., 25(2003), 31--49.
Gutman, I. and Trinajstic, N., "Graph theory and molecular orbitals. Total $pi$-electron energy of alternant hydrocarbons", Chem. Phys. Lett., 17(4)(1972), 535--538.
Gutman, I., "Geometric approach to degree-based topological indices:Sombor indices", textit{MATCH Common, Math. Comput. Chem.,} 86 (2021), 11--16.
Kier, L. B., Hall, L. H., Murray, W. J. and Randi'{c}, M., Molecular Connectivity V: connectivity series concept applied to density, J. Pharm. Sci., 65(1976), 1226--1230.
Kier, L. B. and Hall, L. H., "Molecular Connectivity in Chemistry and Drug Research", Academic Press, New York, 1976.
Li, X. and Zhao, H., "Trees with the first three smallest and largest generalized topological indices", MATCH Commun. Math. Comput. Chem., 50 (2004), 57--62.
Nikmehr, M. J. Veylaki, M. and Soleimani, N., "Some topological indices of V-phenylenic nanotube and nanotori", Optoelectron. Adv. Mater. Rapid Comm., 9(9)(2015), 1147--1149.
Nadeema, M. F., Zafar, S. and Zahidb, Z. "On topological properties of the line graphs of subdivision graphs of certain nanostructures", Appl. Math. Comput., 273 (2016), 125--130.
Randi'{c}, M., "Characterization of molecular branching", J. Am. Chem. Soc., 97 (1975), 6609--6615.
Nadeem, M. F., Zafar, S. and Zahidb, Z., "On certain topological indices of the line graph of subdivision graphs", Appl. Math. Comput., 271(2015), 790--794.
Ranjini, P. S., Lokesha, V. and Cang"{u}l, I. N., "On the Zagreb indices of the line graphs of the subdivision graphs", Appl. Math. Comput., 218}(3) (2011), 699--702.
Ranjini, P. S., Lokesha, V., Rajan, M. A. and Raju, M. P., "On the Shultz index of the subdivision graphs", Adv. Stud. Contemp. Math., (Kyungshang) 21(3)(2011), 279--290.
Su, G. and Xu, L., "Topological indices of the line graph of subdivision graphs and their Schur-bounds",Appl. Math. Comput., 253 (2015), 395--401.