Work place: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo Henan, 454000, China
E-mail: 212110010017@home.hpu.edu.cn
Website:
Research Interests: Combinatorial Optimization
Biography
Xiaohan Ye is currently pursuing a master's degree at the School of Mathematics and Information Science of Henan Polytechnic University in China. Her research interests are graph theory and combinatorial optimization.
DOI: https://doi.org/10.5815/ijmsc.2024.01.01, Pub. Date: 8 Feb. 2024
The symmetry of the graph has always been a hot topic in graph theory and the vertex-transitive graphs are a class of graphs with high symmetry. Cayley graphs which are the highly symmetrical graphs play an important role and much work has been done in the study. The tri-Cayley graph is a natural generalization of the Cayley graph. A graph is said to be a tri-Cayley graph if it admits a semiregular subgroup of automorphisms having three orbits of equal length. Koács et al. classified the cubic symmetric tricirculants in 2012 and Potočnik et al. classified the cubic vertex-transitive tricirculants in 2018. Currently, there is no research on the classification of 4-valent tri-Cayley graphs over cyclic group. In this paper, we will construct two classes of 4-valent tri-Cayley graphs over cyclic group and discuss their automorphism groups. In addition, the vertex transitivity, edge transitivity and arc transitivity are proved.
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