  We consider an infinite graphene geometry where bonds and sites have been
removed selectively to map it onto an effective Sierpinski gasket comprising of
hexagons. We show that such a structure is capable of sustaining an infinite
number of extended single particle states inspite of the absence of any
translational order. When each basic hexagonal plaquette in the Sierpinski
geometry is threaded by a magnetic flux, the spectrum exhibits bands of
extended eigenstates. The bands persist for any arbitrary value of the flux but
disappear again as the flux becomes equal to half the fundamental flux quantum.
The localization - de-localization issues are discussed thoroughly along with
the computation of two terminal magneto-transport of finite versions of the
lattice. The numerical results corroborate our analytical findings.
