TOTAL ZERO DIVISOR GRAPHS OF POLYNOMIAL RINGS
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Published:
Jul 28, 2017
Keywords:
Total zero divisor graph, Polynomial ring, Commutative ring, Diameter, Regular graph.
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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.
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