| Equitable Total Coloring of Fibonacci Graphs |
| Received:January 08, 2023 Revised:November 15, 2023 |
| Key Words:
Fibonacci graph equitable total coloring equitable total chromatic number
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.62072292) and the Natural Science Foundation of Shandong Province (Grant No.ZR2020KF010). |
| Author Name | Affiliation | | Yong LI | School of Information Science and Electricity Engineering, Shandong Jiaotong University, Shandong 250357, P. R. China | | Chunling TONG | School of Information Science and Electricity Engineering, Shandong Jiaotong University, Shandong 250357, P. R. China
Department of Mathematics, Simon Fraser University, BC V5A 1S6, Canada | | Senyuan SU | School of Information Science and Electricity Engineering, Shandong Jiaotong University, Shandong 250357, P. R. China | | Yanan SU | School of Information Science and Electricity Engineering, Shandong Jiaotong University, Shandong 250357, P. R. China |
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| Abstract: |
| 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 $\Delta>=6$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2024.02.001 |
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