Classification of the pentavalent symmetric graphs of order 18p

Classification of the pentavalent symmetric graphs of order 18p

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 18 p , for each prime p . It is shown that, such graphs there exist if and only if p = 2, 7 or 19, and up to i...

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Veröffentlicht in:Indian journal of pure and applied mathematics 2019-06, Vol.50 (2), p.485-497
Hauptverfasser: Alaeiyan, Mehdi, Akbarizadeh, Masoumeh
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Automorphisms
Classification
Graphs
Isomorphism
Mathematics
Mathematics and Statistics
Numerical Analysis
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Zusammenfassung: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 18 p , 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.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-019-0340-9