Total coloring of graphs associated with algebraic structures and ordered structures Total coloring of graphs associated with algebraic structures and ordered structures
In this paper, we prove 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 zero-divisor graphs of finite reduced commutative rings, comaximal ideal graphs, (co-) a...
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| Published in | Indian journal of pure and applied mathematics Vol. 56; no. 2; pp. 535 - 544 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New Delhi
Indian National Science Academy
01.06.2025
Springer Nature B.V |
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| ISSN | 0019-5588 0975-7465 |
| DOI | 10.1007/s13226-023-00500-4 |
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| Abstract | In this paper, we prove 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 zero-divisor graphs of finite reduced commutative rings, comaximal ideal graphs, (co-) annihilating ideal graphs of commutative rings with finitely many ideals and intersection graphs of Artinian principal ideal rings. |
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| AbstractList | In this paper, we prove 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 zero-divisor graphs of finite reduced commutative rings, comaximal ideal graphs, (co-) annihilating ideal graphs of commutative rings with finitely many ideals and intersection graphs of Artinian principal ideal rings. |
| Author | Khandekar, Nilesh Joshi, Vinayak |
| Author_xml | – sequence: 1 givenname: Nilesh orcidid: 0000-0002-7199-0625 surname: Khandekar fullname: Khandekar, Nilesh organization: Department of Mathematics, Savitribai Phule Pune University – sequence: 2 givenname: Vinayak orcidid: 0000-0001-9105-4634 surname: Joshi fullname: Joshi, Vinayak email: vvjoshi@unipune.ac.in, vinayakjoshi111@yahoo.com organization: Department of Mathematics, Savitribai Phule Pune University |
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| Cites_doi | 10.1016/j.disc.2008.11.034 10.1007/s00373-010-0955-4 10.1017/S0004972717000867 10.1016/0021-8693(88)90202-5 10.1142/S1793557118500948 10.1007/BF01885700 10.1007/BFb0092895 10.1007/978-3-030-88410-9 10.1016/j.disc.2009.02.024 10.1142/S1793830914500475 10.1155/2014/896270 10.1090/S0002-9939-1971-0272687-X 10.1112/jlms/s1-42.1.226 10.2478/s12175-014-0221-y 10.1007/s10474-012-0231-6 10.1515/ms-2023-0081 10.1016/j.disc.2013.02.004 10.1007/s00500-020-05344-2 10.1007/s11083-011-9216-2 10.4153/CMB-2016-017-1 10.1142/S0219498812501149 |
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| Copyright | The Indian National Science Academy 2023 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Copyright Springer Nature B.V. 2025 |
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| Keywords | Coloring of a graph 13A70 Zero-divisor graphs Pseudocomplemented poset Total Coloring Conjecture Direct product of posets Comaximal ideal graph Reduced ring 05C15 06A07 |
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| References | MF Atiyah (500_CR4) 1969 Vinayak Joshi (500_CR16) 2012; 29 500_CR9 D Lu (500_CR23) 2010; 26 JD LaGrange (500_CR22) 2013; 313 VG Vizing (500_CR28) 1964; 3 500_CR29 Nilesh Khandekar (500_CR19) 2020; 24 500_CR15 Saeeid Akbari (500_CR2) 2017; 60 500_CR12 Vinayak Joshi (500_CR17) 2014; 64 M Afkhami (500_CR1) 2012; 137 500_CR30 500_CR31 R Halaš (500_CR14) 1993; 29 I Beck (500_CR5) 1988; 116 R Halaš (500_CR13) 2009; 309 PV Venkatanarasimhan (500_CR26) 1971; 28–1 500_CR18 M Behzad (500_CR7) 1967; 42 Sarika Devhare (500_CR11) 2019; 8 500_CR25 500_CR27 Sarika Devhare (500_CR10) 2018; 97 500_CR21 500_CR24 500_CR3 500_CR20 500_CR8 500_CR6 |
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| SubjectTerms | Applications of Mathematics Coloring Commutativity Graphs Mathematics Mathematics and Statistics Numerical Analysis Original Research Rings (mathematics) |
| Subtitle | Total coloring of graphs associated with algebraic structures and ordered structures |
| Title | Total coloring of graphs associated with algebraic structures and ordered structures |
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