Chromatic Zagreb indices for graphical embodiment of colour clusters

Johan Kok, Sudev Naduvath, Muhammad Kamran Jamil

Abstract


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.


Keywords


Graphical embodiments; colour clusters; colour classes; chromatic Zagreb indices.

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DOI: http://dx.doi.org/10.19184/ijc.2019.3.1.6

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