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The Zagreb indices have been introduced by Gutman and Trinajstić as M1(G) = ∑ v∈V (G) (dG(v))2 and M2(G) = ∑ uv∈E(G) dG(u)dG(v), where dG(u) denotes the degree of vertex u. We now define a new version of Zagreb indices as M1 *(G) = ∑ uv∈E(G) [εG(u) + εG(v)] and M2 * (G) = ∑ uv∈E(G) εG(u)εG(v), where εG(u) is the largest distance between u and any other vertex v of G. The goal of this paper is to further the study of these new topological index  

Let G be a graph. The first and second Zagreb index of G is defined as M1(G)= Σ degG(V)2 and M2(G)= Σ degG(u)degG(V) respectively. In this paper we compute Zagreb indices of chain graphs