Existence of solutions to relativistic non-Abelian Chern-Simons-Higgs vortex equations on graphs

Abstract: Let $G=(V,E)$ be a connected finite graph. We study the relativistic non-Abelian Chern-Simons-Higgs vortex equations on the graph $G$. We establish an existence result to the relativistic non-Abelian Chern-Simons-Higgs vortex equations.