The second Zagreb indices of graphs with given degree sequences

The second Zagreb index of a simple undirected graph GG is defined as M2(G)=∑uv∈E(G)d(u)d(v)M2(G)=∑uv∈E(G)d(u)d(v), where d(x)d(x) is the degree of vertex xx in GG. In this paper, we investigate properties of the extremal graphs with the maximum second Zagreb indices with given graphic sequences, in particular graphic bicyclic sequences. Moreover, we obtain the relations of the second Zagreb indices among the extremal graphs with different degree sequences.