The Construction of two classes of 4-valent tri- Cayley Graphs over Cyclic Group
Автор: Xiaohan Ye, Huanzhi Zhang
Журнал: International Journal of Mathematical Sciences and Computing @ijmsc
Статья в выпуске: 1 vol.10, 2024 года.
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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.
Tri-Cayley graph, cyclic group, vertex-transitive, automorphism group, edge-transitive, arc-transitive
Короткий адрес: https://sciup.org/15019070
IDR: 15019070 | DOI: 10.5815/ijmsc.2024.01.01
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