A structural approach to the graceful coloring of a subclass of trees
Let M={1,2,..m} and G be a simple graph. A graceful m-coloring of G is a proper vertex coloring of G using the colors in M which leads to a proper edge coloring using M∖{m} colors such that the associated color of each edge is the absolute difference between their end vertices. The graceful chromati...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023067713 |
| _version_ | 1797669865330311168 |
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| author | Laavanya D Devi Yamini S |
| author_facet | Laavanya D Devi Yamini S |
| author_sort | Laavanya D |
| collection | DOAJ |
| description | Let M={1,2,..m} and G be a simple graph. A graceful m-coloring of G is a proper vertex coloring of G using the colors in M which leads to a proper edge coloring using M∖{m} colors such that the associated color of each edge is the absolute difference between their end vertices. The graceful chromatic number χg(G)= min {m:G admits a gracefulm− coloring }. We prove that 5≤χg(T)≤7, where T is a tree with Δ=4. Furthermore, we categorize the trees into three types along with its characterization and the related coloring algorithm are presented in this study. |
| first_indexed | 2024-03-11T20:51:00Z |
| format | Article |
| id | doaj.art-d3dabee00d30467d9696daa0b4144032 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-03-11T20:51:00Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-d3dabee00d30467d9696daa0b41440322023-10-01T06:00:08ZengElsevierHeliyon2405-84402023-09-0199e19563A structural approach to the graceful coloring of a subclass of treesLaavanya D0Devi Yamini S1Vellore Institute of Technology, Chennai, Tamil Nadu, IndiaCorresponding author.; Vellore Institute of Technology, Chennai, Tamil Nadu, IndiaLet M={1,2,..m} and G be a simple graph. A graceful m-coloring of G is a proper vertex coloring of G using the colors in M which leads to a proper edge coloring using M∖{m} colors such that the associated color of each edge is the absolute difference between their end vertices. The graceful chromatic number χg(G)= min {m:G admits a gracefulm− coloring }. We prove that 5≤χg(T)≤7, where T is a tree with Δ=4. Furthermore, we categorize the trees into three types along with its characterization and the related coloring algorithm are presented in this study.http://www.sciencedirect.com/science/article/pii/S2405844023067713Graceful coloringGraceful chromatic numberColoring algorithmTrees |
| spellingShingle | Laavanya D Devi Yamini S A structural approach to the graceful coloring of a subclass of trees Heliyon Graceful coloring Graceful chromatic number Coloring algorithm Trees |
| title | A structural approach to the graceful coloring of a subclass of trees |
| title_full | A structural approach to the graceful coloring of a subclass of trees |
| title_fullStr | A structural approach to the graceful coloring of a subclass of trees |
| title_full_unstemmed | A structural approach to the graceful coloring of a subclass of trees |
| title_short | A structural approach to the graceful coloring of a subclass of trees |
| title_sort | structural approach to the graceful coloring of a subclass of trees |
| topic | Graceful coloring Graceful chromatic number Coloring algorithm Trees |
| url | http://www.sciencedirect.com/science/article/pii/S2405844023067713 |
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