Zero-divisor graph and comaximal graph of rings of continuous functions with countable range

In this paper, two outwardly different graphs, namely, the zero-divisor graph [Formula: see text] and comaximal of ring all real-valued continuous functions having countable range, defined on any zero-dimensional space text], are investigated. It is observed that these graphs exhibit resemblance, so far as diameters, girths, connectedness, triangulatedness or hypertriangulatedness concerned. However, study reveals an intermediate complemented if only minimal prime ideals compact. Moreover, when its subgraph complemented. On other hand, over-ring latter known to be a text]-space. Indeed, for large class spaces (i.e. perfectly normal, strongly which not P-spaces), seen non-isomorphic. Defining appropriately quotient graph, it utilized establish discrete (= text]) isomorphic, at most countable. Under assumption continuum hypothesis, converse result also shown true.