Geodesic
Hamiltonian Cubic Graphs and Centralizers of Involutions
Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 458-464

Voir la notice de l'article provenant de la source Cambridge University Press

In 1948, R. Frucht [5] proved that, given a finite group G, there are infinitely many connected cubic graphs X such that the automorphism group Aut X is isomorphic to G. In a letter, Professor Frucht has proposed the problem, whether in addition X can be required to be hamiltonian. One of the aims of the present note is to answer this question affirmatively.THEOREM 1.1. Given a finite group G there are infinitely many finite hamiltonian cubic graphs Y such that Aut Y ≌ G.In fact, we prove the following:THEOREM 1.2. Given a finite cubic graph X having no component isomorphic to K 4, there exists a hamiltonian cubic graph Y such that Aut Y ≌ Aut X and |V(Y)| = 6|V(X)|.This implies 1.1 by the theorem of Frucht [5] mentioned above. 
Babai, László; Frankl, Péter; Kollár, János; Sabidussi, Gert. Hamiltonian Cubic Graphs and Centralizers of Involutions. Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 458-464. doi: 10.4153/CJM-1979-051-8
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