A multi-trace surface integral equation (MT-SIE) solver is proposed to analyze electromagnetic field interactions on composite devices involving magnetized and non-magnetized graphene sheets. The computation domain is decomposed into two subdomains: an exterior subdomain that represents the unbounded background medium where the device resides in and an interior subdomain that represents the dielectric substrate. Resistive Robin transmission conditions (RRTCs) are formulated to describe the infinitesimally thin graphene sheet that partially covers the surface between the two subdomains. On the rest of this surface, traditional Robin transmission conditions (RTCs) are enforced. The electric and magnetic field equations are used as the governing equations in each subdomain. The governing equations of a subdomain are locally coupled to the governing equations of its neighbour using RRTCs and RTCs. The accuracy and the applicability of the proposed MT-SIE solver are demonstrated by various numerical examples.