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Alaeiyan, Mehdi; Akbarizadeh, Masoumeh

Classification of the pentavalent symmetric graphs of order \(18p\). (English) Zbl 1429.05086

Indian J. Pure Appl. Math. 50, No. 2, 485-497 (2019).
Summary: A graph is symmetric if its automorphism group is transitive on the arc set of the graph. In this paper, we give a complete classification of connected pentavalent symmetric graphs of order \(18p\), for each prime \(p\). It is shown that, such graphs there exist if and only if \(p = 2, 7\) or 19, and up to isomorphism, there are only four such graphs.

Cited in 3 Documents

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
05C40 Connectivity

Keywords:

pentavalent symmetric graph; connected graph; arc-transitive graph; automorphism group

Software:

Magma
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Full Text: DOI

References:

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