Academic Journal
Vertex‐Distinguishing and Sum‐Distinguishing Edge Coloring of Regular Graphs.
| Title: | Vertex‐Distinguishing and Sum‐Distinguishing Edge Coloring of Regular Graphs. |
|---|---|
| Authors: | Gao, Yuping1 (AUTHOR) gaoyp@lzu.edu.cn, Shan, Songling2 (AUTHOR), Wang, Guanghui3,4 (AUTHOR) |
| Source: | Journal of Graph Theory. Sep2026, Vol. 113 Issue 1, p73-87. 15p. |
| Subject Terms: | *Regular graphs, *Graph coloring, *Graph theory |
| Abstract: | Given an integer k≥1, an edge‐k‐coloring of a graph G is an assignment of k colors 1,...,k to the edges of G such that no two adjacent edges receive the same color. A vertex‐distinguishing (resp. sum‐distinguishing) edge‐k‐coloring of G is an edge‐k‐coloring such that for any two distinct vertices u and v, the set (resp. sum) of colors taken from all the edges incident with u is different from that taken from all the edges incident with v. The vertex‐distinguishing chromatic index (resp. sum‐distinguishing chromatic index), denoted χvd′(G) (resp. χsd′(G)), is the smallest value k such that G has a vertex‐distinguishing edge‐k‐coloring (resp. sum‐distinguishing edge‐k‐coloring). Let G be a d‐regular graph on n vertices, where n is even and sufficiently large. We show that χvd′(G)=d+2 if d is arbitrarily close to n/2 from above, and χsd′(G)=d+2 if d≥2n3. Our first result strengthens a result of Balister et al. for such class of regular graphs, and our second result constitutes a significant advancement in the field of sum‐distinguishing edge coloring. To achieve these results, we introduce novel edge coloring results which may be of independent interest. [ABSTRACT FROM AUTHOR] |
| Database: | Academic Search Index |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:asx&genre=article&issn=03649024&ISBN=&volume=113&issue=1&date=20260901&spage=73&pages=73-87&title=Journal of Graph Theory&atitle=Vertex%E2%80%90Distinguishing%20and%20Sum%E2%80%90Distinguishing%20Edge%20Coloring%20of%20Regular%20Graphs.&aulast=Gao%2C%20Yuping&id=DOI:10.1002/jgt.70049 Name: Full Text Finder (for New FTF UI) (ns324271) Category: fullText Text: Full Text Finder MouseOverText: Full Text Finder |
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| Items | – Name: Title Label: Title Group: Ti Data: Vertex‐Distinguishing and Sum‐Distinguishing Edge Coloring of Regular Graphs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gao%2C+Yuping%22">Gao, Yuping</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gaoyp@lzu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Shan%2C+Songling%22">Shan, Songling</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Guanghui%22">Wang, Guanghui</searchLink><relatesTo>3,4</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Graph+Theory%22">Journal of Graph Theory</searchLink>. Sep2026, Vol. 113 Issue 1, p73-87. 15p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Regular+graphs%22">Regular graphs</searchLink><br />*<searchLink fieldCode="DE" term="%22Graph+coloring%22">Graph coloring</searchLink><br />*<searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Given an integer k≥1, an edge‐k‐coloring of a graph G is an assignment of k colors 1,...,k to the edges of G such that no two adjacent edges receive the same color. A vertex‐distinguishing (resp. sum‐distinguishing) edge‐k‐coloring of G is an edge‐k‐coloring such that for any two distinct vertices u and v, the set (resp. sum) of colors taken from all the edges incident with u is different from that taken from all the edges incident with v. The vertex‐distinguishing chromatic index (resp. sum‐distinguishing chromatic index), denoted χvd′(G) (resp. χsd′(G)), is the smallest value k such that G has a vertex‐distinguishing edge‐k‐coloring (resp. sum‐distinguishing edge‐k‐coloring). Let G be a d‐regular graph on n vertices, where n is even and sufficiently large. We show that χvd′(G)=d+2 if d is arbitrarily close to n/2 from above, and χsd′(G)=d+2 if d≥2n3. Our first result strengthens a result of Balister et al. for such class of regular graphs, and our second result constitutes a significant advancement in the field of sum‐distinguishing edge coloring. To achieve these results, we introduce novel edge coloring results which may be of independent interest. [ABSTRACT FROM AUTHOR] |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/jgt.70049 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 73 Subjects: – SubjectFull: Regular graphs Type: general – SubjectFull: Graph coloring Type: general – SubjectFull: Graph theory Type: general Titles: – TitleFull: Vertex‐Distinguishing and Sum‐Distinguishing Edge Coloring of Regular Graphs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gao, Yuping – PersonEntity: Name: NameFull: Shan, Songling – PersonEntity: Name: NameFull: Wang, Guanghui IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 03649024 Numbering: – Type: volume Value: 113 – Type: issue Value: 1 Titles: – TitleFull: Journal of Graph Theory Type: main |
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