We determine the full automorphism group of each member of threeinfinite families of connected cubic graphs which are snarks. A graph issaid to be nearly hamiltonian if it has a cycle which contains all verticesbut one. We prove, in particular, that for every possible order n > 28 thereexists a nearly hamiltonian snark of order n with trivial automorphismgroup.
SOME INFINITE CLASSES OF ASYMMETRICNEARLY HAMILTONIAN SNARKS / Fiori, Carla; Ruini, Beatrice. - In: LE MATEMATICHE. - ISSN 0373-3505. - STAMPA. - 65:(2010), pp. 3-21.
SOME INFINITE CLASSES OF ASYMMETRICNEARLY HAMILTONIAN SNARKS
FIORI, Carla;RUINI, Beatrice
2010
Abstract
We determine the full automorphism group of each member of threeinfinite families of connected cubic graphs which are snarks. A graph issaid to be nearly hamiltonian if it has a cycle which contains all verticesbut one. We prove, in particular, that for every possible order n > 28 thereexists a nearly hamiltonian snark of order n with trivial automorphismgroup.
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