2016/12/07 by Shaohui Wang, Wang, Shaohui, Wei Gao +7
Chemistry · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Molecular spectroscopy and chirality #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.1612.02361
openalex publication_date 2016/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The hyper Zagreb index is a kind of extensions of Zagreb index, used for predicting physicochemical properties of organic compounds. Given a graph G= (V(G), E(G)), the first hyper-Zagreb index is the sum of the square of edge degree over edge set E(G) and defined as HM1(G)=∑e=uv∈ E(G)d(e)2, where d(e)=d(u)+d(v) is the edge degree. In this work we define the second hyper-Zagreb index on the adjacent edges as HM2(G)=∑e∼ fd(e)d(f), where e∼ f represents the adjacent edges of G. By inequalities, we explore some upper and lower bounds of these hyper-Zagreb indices, and provide the relation between Zagreb indices and hyper Zagreb indices.