TOTAL ZERO DIVISOR GRAPHS OF POLYNOMIAL RINGS

Abstract

In this paper, we study the total zero divisor graph of polynomial rings. In this if Z(R)[x] is an ideal of R[x], then we discuss the completeness of Z(Γ(R[x])) and Z(Γ(R[[x]])) and also we find diam(Z(Γ(R[x]))) = 3. Further we prove that let R be a finite commutative ring such that Z(R) is not an ideal of R then Reg(G(R[x]) is connected and diam(Reg(G(R[x])) ≤ 2.