Molecular Trees with Extremal Values of the Second Sombor Index
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Authors: Z. TANG AND H. DENG
DOI: 10.46793/KgJMat2607.1161T
Abstract:
A new geometric background of graph invariants was introduced by Gutman, of which the simplest is the second Sombor index SO2, defined as SO2 = SO2(G) = ∑ uv∈E
, where G = (V,E) is a simple graph and
dG(v) denotes the degree of v in G. In this paper, the chemical applicability of the
second Sombor index is investigated and it is shown that the second Sombor index is
useful in predicting physicochemical properties with high accuracy compared to
some well-established and often used indices. Also, we obtain a bound for
the second Sombor index among all (molecular) trees with fixed numbers
of vertices, and characterize those molecular trees achieving the extremal
value.
Keywords:
Second Sombor index, tree, molecular tree, extremal value.
References:
[1] I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (1) (2021) 11–16.
[2] I. Gutman, Sombor indices-back to geometry, Open J. Discrete Appl. Math. 5(2) (2022) 1–5.
[3] I. Gutman, Degree-based topological indices, Croatica Chemica Acta 86 (2013), 351–361.
[4] V. R. Kulli, Graph indices, in: M. Pal, S. Samanta, A. Pal (Eds.), Handbook of Research of Advanced Applications of Graph Theory in Modern Society, Hershey: Global, 2020, 66–91.
[5] R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics, Weinheim, Wiley-VCH, 2009.
[6] H. Deng, Z. Tang and R. Wu, Molecular trees with extremal values of Sombor indices, Int. J. Quantum Chem. 121 (2021), Article ID e26622.
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