On reformulated Zagreb indices

AbstractThe first and second reformulated Zagreb indices are defined respectively in terms of edge-degrees as EM1(G)=∑e∈Edeg(e)2 and EM2(G)=∑e∼fdeg(e)deg(f), where deg(e) denotes the degree of the edge e, and e∼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