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  
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 NameAffiliation
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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