2020/06/16 by Mingyao Zeng, Zeng, Mingyao, Hanyuan Deng +1
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Synthesis and Properties of Aromatic Compounds #Topological and Geometric Data Analysis #math.CO
paper · pdf · doi:10.48550/arxiv.2006.08892
arxiv created 2020/06/16 · openalex publication_date 2020/06/16 · arxiv updated 2020/06/17 · openalex created_date 2020/06/19 · openalex updated_date 2026/07/28
The second Zagreb index is M2(G)=∑uv∈ E(G)dG(u)dG(v). It was found to occur in certain approximate expressions of the total π-electron energy of alternant hydrocarbons and used by various researchers in their QSPR and QSAR studies. Recently the exponential of a vertex-degree-based topological index was introduced. It is known that among all trees with n vertices, the exponential of the second Zagreb index eM2 attains its minimum value in the path Pn. In this paper, we show that eM2 attains its maximum value in the balanced double star with n vertices and solve an open problem proposed by Cruz and Rada [R. Cruz, J. Rada, The path and the star as extremal values of vertex-degree-based topological indices among trees, MATCH Commun. Math. Comput. Chem. 82 (3) (2019) 715-732].