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The study of graph theory was introduced and widely researched since many practical problems can be represented by graphs. A non-zero divisor graph is a graph in which its set of vertices is the non-zero elements of the ring and the vertices  x  and  y  are adjacent if and only if  xy  ≠ 0. In this study, we introduced the non-zero divisor graphs of some finite commutative rings in specific the ring of in tegers modulo 6, ℤ 6  and ring of Hamiltonian quaternion, ℍ(ℤ 2 ). First, the non-zero divisors of the commutative rings are found. Then, the non-zero divisor graphs are constructed. Finally, some properties of the graph, including the chromatic number, clique number, girth and the diameter are obtained.

The non-zero divisor graph of ring of integers modulo six and the Hamiltonian quaternion over integers modulo two