English

A note on chromatic blending of colour clusters

General Mathematics 2017-02-08 v1

Abstract

For a colour cluster \C=(C1,C2,C3,,C)\C =(\mathcal{C}_1,\mathcal{C}_2, \mathcal{C}_3,\dots,\mathcal{C}_\ell), Ci\mathcal{C}_i is a colour class, and Ci=ri1|\mathcal{C}_i|=r_i \geq 1, we investigate a simple connected graph structure G\CG^{\C}, which represents a graphical embodiment of the colour cluster such that the chromatic number χ(G\C)=,\chi(G^{\C})= \ell, and the number of edges is a maximum, denoted ε+(G\C)\varepsilon^+(G^{\C}). We also extend the study by inducing new colour clusters recursively by blending the colours of all pairs of adjacent vertices. Recursion repeats until a maximal homogeneous blend between all \ell colours is obtained. This is called total chromatic blending. Total chromatic blending models for example, total genetic, chemical, cultural or social orderliness integration.

Keywords

Cite

@article{arxiv.1702.00103,
  title  = {A note on chromatic blending of colour clusters},
  author = {Johan Kok and Naduvath Sudev and Muhammad Kamran Jamil},
  journal= {arXiv preprint arXiv:1702.00103},
  year   = {2017}
}

Comments

6 Pages, communicated

R2 v1 2026-06-22T18:06:02.457Z