On semisymmetric cubic graphs of order 20p^2, p prime | Zendy

M. R. Darafsheh | Zendy; M. Shahsavaran | Zendy

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On semisymmetric cubic graphs of order 20p^2, p prime

Author(s) -

M. R. Darafsheh,

M. Shahsavaran

Publication year - 2019

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.2213

Subject(s) - mathematics , prime (order theory) , combinatorics , cubic graph , order (exchange) , discrete mathematics , graph , line graph , voltage graph , finance , economics

A simple graph is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be an arbitrary prime. Folkman proved [Regular line-symmetric graphs, J. Combin. Theory 3 (1967) 215–232] that there is no semisymmetric graph of order 2p or 2p. In this paper an extension of his result in the case of cubic graphs of order 20p is given. We prove that there is no connected cubic semisymmetric graph of order 20p or, equivalently, that every connected cubic edge-transitive graph of order 20p is necessarily symmetric.

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