On Chromatic Zagreb Indices of Certain Graphs

TL;DR

This paper introduces chromatic Zagreb indices, a variation of classical graph invariants based on proper vertex coloring, and explores the concept of chromatically stable graphs.

Contribution

It defines chromatic Zagreb indices and introduces the concept of chromatically stable graphs, extending the classical Zagreb indices with coloring considerations.

Findings

Defined chromatic Zagreb indices in terms of vertex coloring

Introduced the concept of chromatically stable graphs

Extended classical Zagreb indices to colored graphs

Abstract

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.