On chromatic Zagreb indices of certain graphs

Let G be a finite and simple undirected connected graph of order n ≥ 1 and let φ be a proper vertex colouring of G. Denote φ : vi 7→ cj simply, c(vi) = cj . In this paper, we introduce a variation of the well-known Zagreb indices by utilising the parameter c(v) instead of the invariant d(v) for all vertices of G. The new indices are called chromatic Zagreb indices. We study these new indices for certain classes of graphs and introduce the notion of chromatically stable graphs.

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