A refined classification of symmetric cubic graphs
نویسندگان
چکیده
منابع مشابه
Cubic symmetric graphs of orders $36p$ and $36p^{2}$
A graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. In this paper, we classifyall the connected cubic symmetric graphs of order $36p$ and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.
متن کاملA more detailed classification of symmetric cubic graphs
A graph Γ is symmetric if its automorphism group acts transitively on the arcs of Γ, and s-regular if its automorphism group acts regularly on the set of s-arcs of Γ. Tutte (1947, 1959) showed that every cubic finite symmetric cubic graph is s-regular for some s ≤ 5. Djokovič and Miller (1980) proved that there are seven types of arc-transitive group action on finite cubic graphs, characterised...
متن کاملClassification of Cubic Symmetric Tricirculants
A tricirculant is a graph admitting a non-identity automorphism having three cycles of equal length in its cycle decomposition. A graph is said to be symmetric if its automorphism group acts transitively on the set of its arcs. In this paper it is shown that the complete bipartite graph K3,3, the Pappus graph, Tutte’s 8-cage and the unique cubic symmetric graph of order 54 are the only connecte...
متن کاملcubic symmetric graphs of orders $36p$ and $36p^{2}$
a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we classifyall the connected cubic symmetric graphs of order $36p$ and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.
متن کاملSymmetric cubic graphs of small girth
A graph Γ is symmetric if its automorphism group acts transitively on the arcs of Γ, and s-regular if its automorphism group acts regularly on the set of s-arcs of Γ. Tutte (1947, 1959) showed that every cubic finite symmetric cubic graph is s-regular for some s ≤ 5. We show that a symmetric cubic graph of girth at most 9 is either 1-regular or 2-regular (following the notation of Djokovic), or...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.03.011