Chromatic Zagreb indices for graphical embodiment of colour clusters

Johan Kok (1) , Sudev Naduvath (1) , Muhammad Kamran Jamil (2)

1 Christ University, Bangalore
2 Riphah International University

For a colour cluster C = (C 1 , C 2 , C 3 ,. .. , C), 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 G C 1 , G C 2 which represent graphical embodiments of the colour cluster such that the chromatic numbers χ(G C 1) = χ(G C 2) = and min{ε(G C 1)} = min{ε(G C 2)} = i=1 r i − 1, and ε(G) is the size of a graph G. In this paper, we also discuss the chromatic Zagreb indices corresponding to G C 1 , G C 2 .

Mots clés: Graphical embodiments; colour classes; colour clusters; chromatic Zagreb indices

Domaines: Combinatoire [math.CO]

Johan Kok, Sudev Naduvath, Muhammad Kamran Jamil. Chromatic Zagreb indices for graphical embodiment of colour clusters. Indonesian Journal of Combinatorics, 2019, 3 (1), pp.48-62. ⟨10.19184/ijc.2019.3.1.6⟩. ⟨hal-02263300⟩