The classical first and second Zagreb indices of a graph G are defined as M-1(G) = Sigma(u is an element of V) d(G)(v)(2) and M-2(G) = Sigma(uv is an element of E(G)) d(G)(u) d(G)(v), where d(G)(v) is the degree of the vertex v of graph G. The reduced second Zagreb index of a graph G is defined as MR2(G) = Sigma(uv is an element of E(G)) (d(G)(u)-1)(d(G)(u)-1). Recently, the reduced second Zagreb index and difference of Zagreb indices of trees were studied. In this paper, we determine the graphs having maximum and minimum reduced second Zagreb index in the class of cyclic graphs of order n with k cut edges. Moreover difference of the classical Zagreb indices are studied.
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