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Let R be an Artinian ring and G be the compressed zero-divisor graphassociated to R. The question of when the clique number of compressedzero-divisor graphs is finite was raised by J. Coykendall, S. Sather-Wagstaff,L. Sheppardson, and S. Spiroff, in their survey paper entitled On Zero-divisorGraphs. They proved that if length of R is at most four then the clique numberis finite. In the length six case they gave an example of a ring where theclique is infinite. In this paper we show that when length of ring is five thenthe clique number of compressed zero-divisor graph is finite.

On the problem of the finiteness of the compressed zero divisor graphs of Artinian rings