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We study solutions for boson stars in the multi-scalar field theory withglobal symmetry $[U(1)]^N$. The properties of the boson stars are investigatedby the Newtonian approximation with the large coupling limit. Our purpose is tostudy the models bringing about exotic mass distributions which explain flatrotation curves of galaxies. We propose plausible models in which couplingmatrices are associated with various graphs in graph theory.

A Newtonian Analysis of Multi-scalar Boson Stars with Large Self-couplings