C* (X) from a graphical point of view

In this paper, we define a graph called the chain-link graph ?(C*(X)) on the ring C*(X) of all real-valued, bounded, continuous functions defined over a Tychonoff space X. We briefly study some aspects like connectedness, diameter, radius, cycles, chords, dominating sets etc. of ?(C*(X)) and some of its subgraphs. We also inspect the relation between the ideals of C* (X) and the cliques of ?(C*(X)) and finally provide a characterization for all maximal cliques of ?(C*(X)). In the sequel, we prove that there are at least 2c many different maximal cliques, which are never graph isomorphic to each other. Moreover, we inquire about the topological and algebraic notions linked to the neighbourhood of a vertex of the graph. We then observe the correspondence between graph isomorphisms on ?(C*(X)), ring isomorphisms on C*(X) and homeomorphims on X when the topology of X is suitably chosen.