2022/08/19 by Zikai Tang, Tang, Zikai, Hanyuan Deng +1
Chemistry · Computer Science · Mathematics · #Chemical Thermodynamics and Molecular Structure #Combinatorics (math.CO) #Computational Drug Discovery Methods #FOS: Mathematics #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2208.09154
openalex publication_date 2022/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(|d2G(u)-d2G(v)|)/(d2G(u)+d2G(v)), 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 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.