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A note on chromatic blending of colour clusters. (English) Zbl 1449.05101

Summary: For a colour cluster \(\mathbb{C} = ({{\mathcal{C}_1}, {\mathcal{C}_2}, {\mathcal{C}_3}, \ldots, {\mathcal{C}_\ell}})\), \({\mathcal{C}_i}\) is a colour class, and \(|{\mathcal{C}_i}| = {r_i} \ge 1\). We investigate a simple connected graph structure \({G^\mathbb{C}}\), which represents a graphical embodiment of the colour cluster such that the chromatic number \(\chi ({G^\mathbb{C}}) = \ell \), and the number of edges is a maximum, denoted by \({\varepsilon^+} ({G^\mathbb{C}})\). 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.

MSC:

05C15 Coloring of graphs and hypergraphs
05C75 Structural characterization of families of graphs
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