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On the intersection graph of gamma sets in the zero-divisor graph

T. Tamizh Chelvam

Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India

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and

K. Selvakumar

Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India

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https://doi.org/10.1142/S1793830914500670Cited by:5 (Source: Crossref)

Abstract

Let R be a commutative ring. The intersection graph of gamma sets in the zero-divisor graph Γ(R) of R is the graph I_Γ(R) with vertex set as the collection of all gamma sets of the zero-divisor graph Γ(R) of R and two distinct vertices A and B are adjacent if and only if A ∩ B ≠ ∅. In this paper, we study about various properties of I_Γ(R) and investigate the interplay between the graph theoretic properties of I_Γ(R) and the ring theoretic properties of R.

Keywords:

AMSC: 05C99, 05C15, 13A99

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