On $J$-Colouring of Chithra Graphs

Kok, Johan; Naduvath, Sudev

doi:10.48550/arxiv.1808.08661

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Chromatic Completion and Stability In Respect Of J -Colouring1

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2018

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“…Clearly, we have by analogy that, ζ ϕ (G) ≤ ζ(G). We further generalise to a recently introduced colouring convention called Johan colouring or J -colouring [6,7,8,11]. The chromatic completion edge set denoted by E J (G), will be investigated.…”

Section: Chromatic Completion and Stability In Respect Of J -Colouringmentioning

confidence: 99%

Stability in Respect of Chromatic Completion of Graphs

Mphako-Banda,

Kok

2018

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In an improper colouring an edge uv for which, c(u) = c(v) is called a bad edge. The notion of the chromatic completion number of a graph G denoted by ζ(G), is the maximum number of edges over all chromatic colourings that can be added to G without adding a bad edge. We introduce stability of a graph in respect of chromatic completion. We prove that the set of chromatic completion edges denoted by E χ (G), which corresponds to ζ(G) is unique if and only if G is stable in respect of chromatic completion. Thereafter, chromatic completion and stability is discussed in respect of Johan colouring. The difficulty of studying chromatic completion with regards to graph operations is shown by presenting results for two elementary graph operations.

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Section: Chromatic Completion and Stability In Respect Of J -Colouringmentioning

confidence: 99%