On Rings Whose Annihilating-Ideal Graphs Are Blow-Ups of a Class of Boolean Graphs

Guo, Jin Yun; Wu, Tongsuo; Yu, Haisheng

doi:10.4134/jkms.j160283

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Clearly Clique(g) χ(G)1

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2018

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Cited by 2 publications

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“…In [7,8], the studying annihilating-ideal graph of commutative rings were started. On later, this investigation was continued in many papers, for instance see [1,13,14,10,2,12,15].…”

Section: Clearly Clique(g) χ(G)mentioning

confidence: 99%

Annihilating-Ideal Graph of $C(X)$

Badie

2018

Preprint

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In this article we study the annihilating-ideal graph of the ring C(X). We have tried to associate the graph properties of AG(X), the ring properties of C(X) and the topological properties of X. We have shown that X has an isolated point if and only if R is a direct summand of C(X) if and only if AG(X) is not triangulated. Radius, girth, dominating number and clique number of the AG(X) are investigated. We have proved that c(X) dt(AG(X)) w(X) and cliqueAG(X) = χAG(X) = c(X).

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“…In [7,8], the studying annihilating-ideal graph of commutative rings were started. On later, this investigation was continued in many papers, for instance see [1,13,14,10,2,12,15].…”

Section: Clearly Clique(g) χ(G)mentioning

confidence: 99%

Annihilating-Ideal Graph of $C(X)$

Badie

2018

Preprint

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“…In [7], we will use the characterizations to study annihilating ideal graphs of rings which are blow-ups of Boolean graphs (complemented graphs, respectively).…”

Section: Complemented Graphmentioning

confidence: 99%

Complemented graphs and blow-ups of Boolean graphs, with applications to co-maximal ideal graphs

Guo

2015

Filomat

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For a set X, let 2X be the power set of X. Let BX be the Boolean graph, which is defined on the vertex set 2X \ {X, ?}, with M adjacent to N if M ? N = ?. In this paper, several purely graph-theoretic characterizations are provided for blow-ups of a finite or an infinite Boolean graph (respectively, a preatomic graph). Then the characterizations are used to study co-maximal ideal graphs that are blow-ups of Boolean graphs (pre-atomic graphs, respectively).

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On Rings Whose Annihilating-Ideal Graphs Are Blow-Ups of a Class of Boolean Graphs

Cited by 2 publications

References 0 publications

Annihilating-Ideal Graph of $C(X)$

Annihilating-Ideal Graph of $C(X)$

Complemented graphs and blow-ups of Boolean graphs, with applications to co-maximal ideal graphs

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