On Chromatic Zagreb Indices of Certain Graphs
  In this paper we introduce a variation of the well-known Zagreb indices by considering a proper vertex colouring of a graph $G$. The chromatic Zagreb indices are defined in terms of the parameter $c(v), v \in V(G)$ instead of the invariant $d_G(v)$. The notion of chromatically stable graphs is also introduced. 
Johan Kok, N.K. Sudev, U. Mary
math.GM