On Perfect Co-Annihilating-Ideal Graph of a Commutative Artinian Ring

Mirghadim, S. M. Saadat; Nikmehr, M. J.; Nikandish, Reza

doi:10.46793/kgjmat2101.063m

Cited by 2 publications

(2 citation statements)

References 10 publications

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“…The perfectness of AG(R) is studied in [1,Corollary 2.3]. The Corollary 6.16 and Corollary 6.17 are essentially proved for co-annihilating ideal graph in [38]. Corollary 6.17.…”

Section: The Zero-divisor Graph Of a Reduced Ringmentioning

confidence: 99%

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Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures

Khandekar¹,

Joshi²

2022

Preprint

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In this paper, we characterize chordal and perfect zero-divisor graphs of finite posets. Also, it is proved that the zero-divisor graphs of finite posets and the complement of zero-divisor graphs of finite 0-distributive posets satisfy the Total Coloring Conjecture. These results are applied to the zero-divisor graphs of finite reduced rings, the comaximal ideal graph of rings, the annihilating ideal graphs, the intersection graphs of ideals of rings, and the intersection graphs of subgroups of cyclic groups. In fact, it is proved that these graphs associated with a commutative ring R with identity can be effectively studied via the zero-divisor graph of a specially constructed poset from R.

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“…The perfectness of AG(R) is studied in [1,Corollary 2.3]. The Corollary 6.16 and Corollary 6.17 are essentially proved for co-annihilating ideal graph in [38]. Corollary 6.17.…”

Section: The Zero-divisor Graph Of a Reduced Ringmentioning

confidence: 99%

“…For instance, it is known that the class of chordal graphs is perfect; see Dirac [17]. The notion of perfectness, weakly perfectness and chordalness of graphs associated with algebraic structures has been an active area of research; see [1], [5], [7], [8], [15], [38], [39], [42], etc.…”

Section: Introductionmentioning

confidence: 99%

Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures

Khandekar¹,

Joshi²

2022

Preprint

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Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures

Khandekar,

Joshi

2023

Mathematica Slovaca

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In this paper, we characterize the perfect zero-divisor graphs and chordal zero-divisor graphs (its complement) of ordered sets. These results are applied to the zero-divisor graphs of finite reduced rings, the comaximal ideal graphs of rings, the annihilating ideal graphs of rings, the intersection graphs of ideals of rings, and the intersection graphs of subgroups of groups. In fact, it is shown that these graphs associated with a commutative ring R with identity can be effectively studied via the zero-divisor graph of a specially constructed poset from R.

show abstract

On Perfect Co-Annihilating-Ideal Graph of a Commutative Artinian Ring

Cited by 2 publications

References 10 publications

Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures

Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures

Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures

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