Volume : II, Issue : IX, September - 2013

Total Zero Divisor Graph of a Commutative Ring

D. Eswara Rao, D. Bharathi

Abstract :

Let R be a commutative ring with Z(R), its set of zero divisors. The total zero divisor graph of R, denoted Z(Γ(R)) is the undirected (simple) graph with vertices Z(R)*=Z(R)–{0}, the set of nonzero zero divisors of R. and for distinct x, y ∈ z(R)*, the vertices x and y are adjacent if and only if x + y ∈ z(R). In this paper, we study if Z(Γ(R)) is finite and every vertex of Z(Γ(R)) has a finite degree then R is finite and also prove that Z(Γ(R)) connected with diam ≤ 3.

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Article: Download PDF   DOI : 10.36106/ijsr  

Cite This Article:

D.Eswara Rao, D. Bharathi Total Zero Divisor Graph of a Commutative Ring International Journal of Scientific Research, Vol : 2, Issue : 9 September 2013

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