Note on Ideal Based Zero-Divisor Graph of a Commutative Ring
In this paper, we consider the ideal based zero divisor graph ΓI(R) of a commutative ring R. We discuss some graph theoretical properties of ΓI(R) in relation with zero divisor graph. We also relate certain parameters like vertex chromatic number, maximum degree and minimum degree for the graph ΓI(R...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2017-12-01
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| Series: | Discussiones Mathematicae - General Algebra and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgaa.1273 |
| _version_ | 1797714879429214208 |
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| author | Mallika A. Kala R. Selvakumar K. |
| author_facet | Mallika A. Kala R. Selvakumar K. |
| author_sort | Mallika A. |
| collection | DOAJ |
| description | In this paper, we consider the ideal based zero divisor graph ΓI(R) of a commutative ring R. We discuss some graph theoretical properties of ΓI(R) in relation with zero divisor graph. We also relate certain parameters like vertex chromatic number, maximum degree and minimum degree for the graph ΓI(R) with that of Γ(R/I ). Further we determine a necessary and sufficient condition for the graph to be Eulerian and regular. |
| first_indexed | 2024-03-12T07:58:29Z |
| format | Article |
| id | doaj.art-19f223bb88c148cd86fed135b770071a |
| institution | Directory Open Access Journal |
| issn | 2084-0373 |
| language | English |
| last_indexed | 2024-03-12T07:58:29Z |
| publishDate | 2017-12-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae - General Algebra and Applications |
| spelling | doaj.art-19f223bb88c148cd86fed135b770071a2023-09-02T19:59:44ZengUniversity of Zielona GóraDiscussiones Mathematicae - General Algebra and Applications2084-03732017-12-0137217718710.7151/dmgaa.1273dmgaa.1273Note on Ideal Based Zero-Divisor Graph of a Commutative RingMallika A.0Kala R.1Selvakumar K.2Department of Mathematics Manonmaniam Sundaranar University Tirunelveli 627 012, TamilNadu, IndiaDepartment of Mathematics Manonmaniam Sundaranar University Tirunelveli 627 012, TamilNadu, IndiaDepartment of Mathematics Manonmaniam Sundaranar University Tirunelveli 627 012, TamilNadu, IndiaIn this paper, we consider the ideal based zero divisor graph ΓI(R) of a commutative ring R. We discuss some graph theoretical properties of ΓI(R) in relation with zero divisor graph. We also relate certain parameters like vertex chromatic number, maximum degree and minimum degree for the graph ΓI(R) with that of Γ(R/I ). Further we determine a necessary and sufficient condition for the graph to be Eulerian and regular.https://doi.org/10.7151/dmgaa.1273zero-divisor graphchromatic numberideal based zero divisor graphclique number05c6905c4513a15 |
| spellingShingle | Mallika A. Kala R. Selvakumar K. Note on Ideal Based Zero-Divisor Graph of a Commutative Ring Discussiones Mathematicae - General Algebra and Applications zero-divisor graph chromatic number ideal based zero divisor graph clique number 05c69 05c45 13a15 |
| title | Note on Ideal Based Zero-Divisor Graph of a Commutative Ring |
| title_full | Note on Ideal Based Zero-Divisor Graph of a Commutative Ring |
| title_fullStr | Note on Ideal Based Zero-Divisor Graph of a Commutative Ring |
| title_full_unstemmed | Note on Ideal Based Zero-Divisor Graph of a Commutative Ring |
| title_short | Note on Ideal Based Zero-Divisor Graph of a Commutative Ring |
| title_sort | note on ideal based zero divisor graph of a commutative ring |
| topic | zero-divisor graph chromatic number ideal based zero divisor graph clique number 05c69 05c45 13a15 |
| url | https://doi.org/10.7151/dmgaa.1273 |
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