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Planarity Johan colouring of graphs. (English) Zbl 1382.05027

Summary: In this paper, we have introduced new planarity of Johan colouring of graphs. This concept is motivated by the invariant called Johan colouring of graphs. The study revolves on maximum colouring of graphs. The planarity Johan colouring of the graph \(G\) is defined by planar graph \(G\) and denoted by \(\mathcal{P}(G)\). The planarity of Johan colouring is presented and a number of explicit results for wheel graph, double wheel graph, web graph and helm graph are obtained.

MSC:

05C15 Coloring of graphs and hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C38 Paths and cycles
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