2022/05/30 by Muhuo Liu, Liu, Muhuo, Shumei Pang +5
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #Computational Drug Discovery Methods #FOS: Mathematics #Graph theory and applications #Molecular Junctions and Nanostructures
paper · pdf · doi:10.48550/arxiv.2205.15220
openalex publication_date 2022/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a connected graph G on at least three vertices, the augmented Zagreb index (AZI) of G is defined as AZI(G)=∑uv∈ E(G)((d(u)d(v))/(d(u)+d(v)-2))3, being a topological index well-correlated with the formation heat of heptanes and octanes. A k-apex tree G is a connected graph admitting a k-subset X⊂ V(G) such that G-X is a tree, while G-S is not a tree for any S⊂ V(G) of cardinality less than k. By investigating some structural properties of k-apex trees, we identify the graphs minimizing the AZI among all k-apex trees on n vertices for k≥ 4 and n≥ 3(k+1). The latter solves an open problem posed in [K. Cheng, M. Liu, F. Belardo, \em Appl. Math. Comput., \bf402 (2021), 126139].