Semisymmetric cubic graphs of order $34p^3$
Bull. Korean Math. Soc. 2020 Vol. 57, No. 3, 739-750
https://doi.org/10.4134/BKMS.b190458
Published online January 9, 2020
Printed May 31, 2020
Mohammad Reza Darafsheh, Mohsen Shahsavaran
College of Science; College of Science
Abstract : A simple graph is called semisymmetric if it is regular and edge transitive but not vertex transitive. Let $p$ be a prime. Folkman proved [J.~Folkman, {\it Regular line-symmetric graphs}, Journal of Combinatorial Theory {\bf 3} (1967), no. 3, 215--232] that no semisymmetric graph of order $2p$ or $2p^2$ exists. In this paper an extension of his result in the case of cubic graphs of order $34p^3$, $p\neq 17$, is obtained.
Keywords : Edge-transitive graph, vertex-transitive graph, semisymmetric graph, order of a graph, classification of cubic semisymmetric graphs
MSC numbers : 05E18, 20D60, 05C25, 20B25
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