An Essay on Comp\^onent\u{a} Analysis of Graphs

In most studies related to colouring of graphs and perhaps in the study of other invariants and variants of graphs, the restrictions of non-triviality and connectedness are placed upon graphs. For the introduction to comp^{o}nent\u{a} analysis, these restrictions are relaxed. In particular, this essay focuses on comp^{o}nent\u{a} analysis in respect of the recently introduced $J$-colouring. The concept of $J^c$-rainbow connectivity is also introduced in this paper.