Chromatic Zagreb indices for graphical embodiment of colour clusters

Johan Kok (CHRIST (Deemed to be University) Bangalore)
Sudev Naduvath (Vidya Academy of Science & Technology Thrissur, Kerala, India.)
Muhammad Kamran Jamil (Riphah International University, Lahore)

Indonesian Journal of Combinatorics
Vol 3, No 1 (2019)

For a colour cluster C = (C1, C2, C3, …, Cℓ), where Ci is a colour class such that ∣Ci∣ = ri, a positive integer, we investigate two types of simple connected graph structures G1C, G2C which represent graphical embodiments of the colour cluster such that the chromatic numbers χ(G1C) = χ(G2C) = 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 G1C, G2C.