Chromatic Zagreb indices for graphical embodiment of colour clusters

Abstract

For a colour cluster C = (C₁, C₂, C₃, …, C_ℓ), where C_i is a colour class such that ∣C_i∣ = r_i, a positive integer, we investigate two types of simple connected graph structures G₁^C, G₂^C which represent graphical embodiments of the colour cluster such that the chromatic numbers χ(G₁^C) = χ(G₂^C) = ℓ and $\min\{\varepsilon(G^{C}_1)\}=\min\{\varepsilon(G^{C}_2)\} =\sum\limits_{i=1}^{\ell}r_i-1$, and ɛ(G) is the size of a graph G. In this paper, we also discuss the chromatic Zagreb indices corresponding to G₁^C, G₂^C.