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 |
| Published: |
Elsevier
2023-09-01
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| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023067713 |
| Summary: | 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. |
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| ISSN: | 2405-8440 |