On reformulated Zagreb indices

The first and second reformulated Zagreb indices are defined respectively in terms of edge-degrees as EM1(G)=∑e∈Edeg(e)2EM1(G)=∑e∈Edeg(e)2 and EM2(G)=∑e∼fdeg(e)deg(f)EM2(G)=∑e∼fdeg(e)deg(f), where deg(e)deg(e) denotes the degree of the edge ee, and e∼fe∼f means that the edges ee and ff 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 nn-vertex unicyclic graphs with minimum and maximum first and second Zagreb indices, respectively. Furthermore, we introduce another generalization of Zagreb indices.