On reformulated Zagreb indices

The first and second reformulated Zagreb indices are defined respectively in terms of edge-degrees as EM1(G) = Sigma(e is an element of E) deg(e)(2) and EM2(G) = E-e similar to f deg(e) deg(f), where deg(e) denotes the degree of the edge e, and e similar to f means that the edges e and f are adjacent. We give upper and lower bounds for the first reformulated Zagreb index, and lower bounds for the second reformulated Zagreb index. Then we determine the extremal n-vertex unicyclic graphs with minimum and maximum first and second Zagreb indices, respectively. Furthermore, we introduce another generalization of Zagreb indices. (C) 2011 Elsevier B.V. All rights reserved.