Let L be a lattice. The annihilating-ideal graph of is simple whose vertex set the all nontrivial ideals and two distinct vertices I J are adjacent if only I∧J=0. In this paper, crosscap graphs lattices with at most four atoms characterized. These characterizations provide classes multipartite graphs, which embedded in Klein bottle.

The recently reported result from XENON1T experiment indicates that there is an excess with $3.5\sigma$ significance in the electronic recoil events. Interpreted as new physics, sources are needed to account for scattering. We show a dark fermion $\psi$ mass about $ \mathcal{O}\left(10\right)$ MeV semi-annihilation of $Z_3$ matter $X$ and subsequent decay gauge boson $V_\mu$ may be responsible ...