The Nordhaus–Gaddum-type inequalities for the Zagreb index and co-index of graphs

AbstractLet k≥2 be an integer, a k-decomposition (G1,G2,…,Gk) of the complete graph Kn is a partition of its edge set to form k spanning subgraphs G1,G2,…,Gk. In this contribution, we investigate the Nordhaus–Gaddum-type inequality of a k-decomposition of Kn for the general Zagreb index and a 2-decomposition for the Zagreb co-indices, respectively. The corresponding extremal graphs are characterized