Zero-divisor graphs of reduced Rickart -rings

For a ring with an involution *, the of , Γ*( ), is the graph whose vertices are the nonzero left zero-divisors in such that distinct vertices and are adjacent if and only if * = 0. In this paper, we study the zero-divisor graph of a Rickart *-ring having no nonzero nilpotent element. The distance, diameter, and cycles of Γ*( ) are characterized in terms of the collection of prime strict ideals of . In fact, we prove that the clique number of Γ*( ) coincides with the cellularity of the hullkernel topological space Σ( ) of the set of prime strict ideals of , where cellularity of the topological space is the smallest cardinal number such that every family of pairwise disjoint non-empty open subsets of the space have cardinality at most