The automorphism group of the Petersen graph is known to be isomorphic to the symmetric group on 5 elements. This proof without words provides an insightful and colorful image that proves this fact, without words. The image represents the Petersen graph with the ten 3-element subsets of {1, ...
An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is isomorphic with G. The set of automorphisms defines a permutation group known as
Automorphism groups and the full state spaces of the Petersen graph generalizations of G32The geometric duals of the generalized Petersen graphs G( n, k) are the Greechie representations of the Generalizations of G 32. The duals are denotes by G ( n, k) and the generalizations by L( G ...
It generalizes the Petersen graph, which is obtained if Γ is the pentagon. The automorphism group ofΓΓis described for an arbitrary graph Γ. In particular, it is shown that the ratio between the cardinalities of the automorphism groups ofΓΓand Γ can attain only the values 1, 2, 4...
Automorphism groups and the full state spaces of the Petersen graph generalizations of G32doi:10.1016/0012-365x(88)90092-1Gerald Schrag
This paper considers connected, vertex-transitive graphs X of order at least 3 where the automorphism group of X contains a transitive subgroup G whose commutator subgroup is cyclic of prime-power order. We show that of these graphs, only the Petersen graph is not Hamiltonian....