| 李勇,仝春灵,苏森原,苏亚男.Fibonacci图的等全着色[J].数学研究及应用,2024,44(2):143~151 |
| Fibonacci图的等全着色 |
| Equitable Total Coloring of Fibonacci Graphs |
| 投稿时间：2023-01-08 修订日期：2023-11-15 |
| DOI：10.3770/j.issn:2095-2651.2024.02.001 |
| 中文关键词: Fibonacci图 等全着色 等全色数 |
| 英文关键词:Fibonacci graph equitable total coloring equitable total chromatic number |
| 基金项目:国家自然科学基金(Grant No.62072292),山东省自然科学基金(Grant No.ZR2020KF010). |
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| 中文摘要: |
| 图$G$的等全着色是使得着任意2个颜色的元素数最多差1的全着色,等全着色所需要的最少颜色数叫等全色数.这篇文章研究了Fibonacci图$F_{\Delta,n}$的等全着色,求得了$\Delta=3,4,5$时$F_{\Delta,n}$的等全色数的确切值, 并猜想了$\Delta>=6$时$F_{\Delta,n}$的等全色数. |
| 英文摘要: |
| The equitable total coloring of a graph $G$ is a total coloring such that the numbers of elements in any two colors differ by at most one. The smallest number of colors needed for an equitable total coloring is called the equitable total chromatic number. This paper contributes to the equitable total coloring of Fibonacci graphs $F_{\Delta,n}$. We determine the equitable total chromatic numbers of $F_{\Delta,n}$ for $\Delta=3,4,5$ and propose a conjecture on that for $\Delta>=6$. |
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