Automorphism Group and Fixing Number of (۳,۶)−and (۴,۶)−Fullerene Graphs

چکیده مقاله

The fixing number of a graph Γ is the minimum cardinality of a set S of V(Γ) such that every non-identity automorphism of G moves at least one member of S.In this case, it is easy to see that the automorphism group of the graph obtained from Γ by fixing every node inSis trivial. The aim of this paper is to investigate the automorphism group and fixing number of six families of (3,6)−fullerene graphs. Moreover, an example of an infinite class G[n] of cubic planar n−vertex graphs is presented in which faces are triangles and hexagons. It is proved that the automorphism group of G[n] has order 2n+2 and fixing number n+ 1. This shows that by omitting the condition of 3−connectivity in definition of a fullerene graph, the symmetry group can be enough large.