On acyclic and unicyclic conjugated graphs with maximum Zagreb indices - Li, Shuchao; Zhao, Qin (Utilitas Mathematica, 2011)
For a molecular graph, the first Zagreb index M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we first obtain a sharp upper bound on M1-values of trees in terms of the order and the given size of matching. Then we investigate Zagreb indices of unicyclic conjugated graphs G (i.e., unicyclic graphs with a perfect matching) and a sharp upper bound on M1(G), M2 (G) are determined, respectively. The sharp upper bounds for Zagreb indices of unicyclic graphs in terms of the order and given size of matching are also determined.