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RISS 인기검색어
- 검색키워드
- 저자 : Shokoofe Habibi (검색결과 2 건)
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The total graph of a commutative ring with respect to proper ideals
Ahmad Abbasi,Shokoofe Habibi 대한수학회 2012 대한수학회지 Vol.49 No.1
Let R be a commutative ring and I its proper ideal, let S(I)be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(ΓI (R)). It is the (undirected) graph with all ele-ments of R as vertices, and for distinct x; y 2 R, the vertices x and y are adjacent if and only if x + y 2 S(I). The total graph of a commutative ring, that denoted by T((R)), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y 2 Z(R) which is due to Anderson and Badawi [2]. In the case I = f0g, T(ΓI (R)) = T(Γ(R)); this is an important result on the denition.
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THE TOTAL GRAPH OF A COMMUTATIVE RING WITH RESPECT TO PROPER IDEALS
Abbasi, Ahmad,Habibi, Shokoofe Korean Mathematical Society 2012 대한수학회지 Vol.49 No.1
Let R be a commutative ring and I its proper ideal, let S(I) be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(${\Gamma}_I(R)$). It is the (undirected) graph with all elements of R as vertices, and for distinct x, y ${\in}$ R, the vertices x and y are adjacent if and only if x + y ${\in}$ S(I). The total graph of a commutative ring, that denoted by T(${\Gamma}(R)$), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y ${\in}$ Z(R) which is due to Anderson and Badawi [2]. In the case I = {0}, $T({\Gamma}_I(R))=T({\Gamma}(R))$; this is an important result on the definition.
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