2020/10/08 by Shu‐Yu Cui, Cui, Shu-Yu, Weifan Wang +5 · 2 citations
Computer Science · Mathematics · #05C07 #92E10 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2010.03748
openalex publication_date 2020/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Very recently, the first geometric-arithmetic index GA and arithmetic-geometric index AG were introduced in mathematical chemistry. In the present paper, we first obtain some lower and upper bounds on AG and characterize the extremal graphs. We also establish various relations between AG and other topological indices, such as the first geometric-arithmetic index GA, atom-bond-connectivity index ABC, symmetric division deg index SDD, chromatic number χ and so on. Finally, we present some sufficient conditions of GA(G)>GA(G-e) or AG(G)>AG(G-e) for an edge e of a graph G. In particular, for the first geometric-arithmetic index, we also give a refinement of Bollobás-Erdős-type theorem obtained in [3].