Order-congruence graph, denoted by C_o (Ζ_n ) is a graph associated to the commutative ring Z_n. The elements of the ring Ζ_n are considered as the vertices of C_o (Ζ_n ), where any two distinct vertices a and b are adjacent in C_o (Ζ_n ) whenever a+b≡0(mod n) or a.b≡0(mod n) with b≠n-a, where n is the order of Z_n. In this chapter we explore various properties of C_o (Ζ_n ), it’s line graph and their polynomial representations.