Some Results on Achromatic and b-chromatic Colouring of Graphs of Some Finite Rings

The notion of zero divisor graphs of a commutative ring was first studied by I. Beck [1] in 1988. In his paper on the colouring of commutative rings, Beck discussed the chromatic colouring of these graphs. The concept of identity graphs of commutative rings was later introduced by Vasantha Kandasamy WB. and Florentin Smarandache [2] in 2009. In this paper, the focus is on the achromatic and b-chromatic colouring of zero divisor graphs and identity graphs of certain finite rings. Additionally, the achromatic and b-chromatic numbers of the central graph of these graphs have been explored, thereby establishing a connection between the fields of ring theory and graph theory in terms of colouring.