  Topological semimetals feature a diversity of nodal manifolds including nodal
points, various nodal lines and surfaces, and recently novel quantum states in
non-Hermitian systems have been arousing widespread research interests. In
contrast to Hermitian systems whose bulk nodal points must form closed
manifolds, it is fascinating to find that for non-Hermitian systems exotic
nodal manifolds can be bounded by exceptional points in the bulk band
structure. Such exceptional points, at which energy bands coalesce with band
conservation violated, are iconic for non-Hermitian systems. In this work, we
show that a variety of nodal lines and drumheads with exceptional boundary can
be realized on 2D and 3D honeycomb lattices through natural and physically
feasible non-Hermitian processes. The bulk nodal Fermi-arc and drumhead states,
although is analogous to, but should be essentially distinguished from the
surface counterpart of Weyl and nodal-line semimetals, respectively, for which
surface nodal-manifold bands eventually sink into bulk bands. Then we
rigorously examine the bulk-boundary correspondence of these exotic states with
open boundary condition, and find that these exotic bulk states are thereby
undermined, showing the essential importance of periodic boundary condition for
the existence of these exotic states. As periodic boundary condition is
non-realistic for real materials, we furthermore propose a practically feasible
electrical-circuit simulation, with non-Hermitian devices implemented by
ordinary operational amplifiers, to emulate these extraordinary states.
