  Over half of GeV gamma-ray sources observed by the EGRET experiment have not
yet been identified as known astronomical objects. There is an isotropic
component of such unidentified sources, whose number is about 60 in the whole
sky. Here we calculate the expected number of dynamically forming clusters of
galaxies emitting gamma-rays by high energy electrons accelerated in the shock
wave when they form, in the framework of the standard theory of structure
formation. We find that a few tens of such forming clusters should be
detectable by EGRET and hence a considerable fraction of the isotropic
unidentified sources can be accounted for, if about 5% of the shock energy is
going into electron acceleration. We argue that these clusters are very
difficult to detect in x-ray or optical surveys compared with the conventional
clusters, because of their extended angular size of about 1 degree. Hence they
define a new population of ``gamma-ray clusters''. If this hypothesis is true,
the next generation gamma-ray telescopes such as GLAST will detect more than a
few thousands of gamma-ray clusters. It would provide a new tracer of
dynamically evolving structures in the universe, in contrast to the x-ray
clusters as a tracer of hydrodynamically stabilized systems. We also derive the
strength of magnetic field required for the extragalactic gamma-ray background
by structure formation to extend up to 100 GeV as observed, that is about
10^{-5} of the shock-heated baryon energy density.
