ON THE TOTAL CHROMATIC NUMBER OF ODD LINE GRAPHS OF ODD COMPLETE GRAPHS.
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| Title: | ON THE TOTAL CHROMATIC NUMBER OF ODD LINE GRAPHS OF ODD COMPLETE GRAPHS. |
|---|---|
| Authors: | Thatchayani, S.1 thatchu170@gmail.com, Geethalakshmi, S.1 geetha2611@gmail.com, Somasundaram, K.2 s_sundaram@cb.amrita.edu |
| Source: | Advances & Applications in Discrete Mathematics. Apr2026, Vol. 43 Issue 3, p337-352. 16p. |
| Subjects: | Complete graphs, Graph coloring |
| Abstract: | ≥a total coloring of a graphg = (ν,ε) entails the meticulous assignment of colors to both vertices and edges, ensuring that neither two adjacent vertices nor two adjacent edges receive the same color. furthermore, it requires that for each edge, the colors of its end-points and the edge itself must differ. the total chromatic number of a graph g, indicated as χ"(g) signifies the minimum number of colors required for such a total coloring. the renowned conjecture by behzad and vizing asserts that for any graph g, the inequality Δ (g) + 1 ≤ χ"(g) ≤ Δ(g) + 2 holds, where Δ(g) signifies the graph's maximum degree. in this paper, we obtain that odd line graphs of odd complete graphs L (Kn), where n = 2℘ + 1 and ℘ 3 (with ℘ being odd), can be adorned with a total coloring with Δ(L(Kn)) + 1 colors. [ABSTRACT FROM AUTHOR] |
| Copyright of Advances & Applications in Discrete Mathematics is the property of Pushpa Publishing House and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: ON THE TOTAL CHROMATIC NUMBER OF ODD LINE GRAPHS OF ODD COMPLETE GRAPHS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Thatchayani%2C+S%2E%22">Thatchayani, S.</searchLink><relatesTo>1</relatesTo><i> thatchu170@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Geethalakshmi%2C+S%2E%22">Geethalakshmi, S.</searchLink><relatesTo>1</relatesTo><i> geetha2611@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Somasundaram%2C+K%2E%22">Somasundaram, K.</searchLink><relatesTo>2</relatesTo><i> s_sundaram@cb.amrita.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Advances+%26+Applications+in+Discrete+Mathematics%22">Advances & Applications in Discrete Mathematics</searchLink>. Apr2026, Vol. 43 Issue 3, p337-352. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Complete+graphs%22">Complete graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+coloring%22">Graph coloring</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: ≥a total coloring of a graphg = (ν,ε) entails the meticulous assignment of colors to both vertices and edges, ensuring that neither two adjacent vertices nor two adjacent edges receive the same color. furthermore, it requires that for each edge, the colors of its end-points and the edge itself must differ. the total chromatic number of a graph g, indicated as χ"(g) signifies the minimum number of colors required for such a total coloring. the renowned conjecture by behzad and vizing asserts that for any graph g, the inequality Δ (g) + 1 ≤ χ"(g) ≤ Δ(g) + 2 holds, where Δ(g) signifies the graph's maximum degree. in this paper, we obtain that odd line graphs of odd complete graphs L (Kn), where n = 2℘ + 1 and ℘ 3 (with ℘ being odd), can be adorned with a total coloring with Δ(L(Kn)) + 1 colors. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Advances & Applications in Discrete Mathematics is the property of Pushpa Publishing House and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.17654/0974165826022 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 337 Subjects: – SubjectFull: Complete graphs Type: general – SubjectFull: Graph coloring Type: general Titles: – TitleFull: ON THE TOTAL CHROMATIC NUMBER OF ODD LINE GRAPHS OF ODD COMPLETE GRAPHS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Thatchayani, S. – PersonEntity: Name: NameFull: Geethalakshmi, S. – PersonEntity: Name: NameFull: Somasundaram, K. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 09741658 Numbering: – Type: volume Value: 43 – Type: issue Value: 3 Titles: – TitleFull: Advances & Applications in Discrete Mathematics Type: main |
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