On Certain J-Colouring Parameters of Graphs

In this paper, a new type of colouring called J-colouring is introduced. This colouring concept is motivated by the newly introduced invariant called the rainbow neighbourhood number of a graph. The study ponders on maximal colouring opposed to minimum colouring. An upper bound for a connected graph is presented, and a number of explicit results are presented for cycles, complete graphs, wheel graphs and for a complete l-partite graph.