Classification of cubic vertex-transitive tricirculants
Ars mathematica contemporanea, Tome 18 (2020) no. 1, pp. 1-31
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A finite graph is called a tricirculant if admits a cyclic group of automorphism which has precisely three orbits on the vertex-set of the graph, all of equal size. We classify all finite connected cubic vertex-transitive tricirculants. We show that except for some small exceptions of order less than 54, each of these graphs is either a prism of order 6k with k odd, a Möbius ladder, or it falls into one of two infinite families, each family containing one graph for every order of the form 6k with k odd.
Keywords:
Graph, cubic, semiregular automorphism, tricirculant, vertex-transitive
@article{10_26493_1855_3974_1815_b52,
author = {Primo\v{z} Poto\v{c}nik and Micael Toledo},
title = {
{Classification} of cubic vertex-transitive tricirculants
},
journal = {Ars mathematica contemporanea},
pages = {1--31},
year = {2020},
volume = {18},
number = {1},
doi = {10.26493/1855-3974.1815.b52},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1815.b52/}
}
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Primož Potočnik; Micael Toledo. Classification of cubic vertex-transitive tricirculants. Ars mathematica contemporanea, Tome 18 (2020) no. 1, pp. 1-31. doi: 10.26493/1855-3974.1815.b52
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