Graphs Associated with Finite Zero Ring

This paper introduces the notion of zero ring graphs. Basic properties of the zero ring graphs are investigated and characterization results regarding connect-edness and planarity are given. Further, we determine the chromatic number for ΓM2^0 (Zp [x]/ x^k), where p is a prime, k 1 and it is shown that an isomorphism exists among the zero ring graphs ΓM2^0 (Z_p^k), ΓM2^0 (Zp[x]/ x^k) and ΓM2^0 (F_p^k).