‎Let R be a commutative ring with non-zero identity‎. ‎The‎ ‎cozero-divisor graph of R, ‎denoted by \Gamma'(R), ‎is a graph‎ ‎with vertices in W^*(R), ‎which is the set of all non-zero and‎ ‎non-unit elements of R, ‎and two distinct vertices a and b in‎ W^*(R) are adjacent if and only if a\notin bR and b\notin‎ ‎aR. ‎In this paper‎, ‎we investigate some combinatorial properties‎ ‎of the cozero-divisor graphs \Gamma'(R[x]) and‎ \Gamma'(R[[x]]) such as connectivity‎, ‎diameter‎, ‎girth‎, ‎clique‎ ‎numbers and planarity‎. ‎We also study the cozero-divisor graphs of‎ ‎the direct products of two arbitrary commutative rings‎.

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