We analyze how the permittivity of a circular dielectric rod influences the total scattering cross-section (TSCS), the absorption cross-section (ACS), and the extinction cross-section (ECS) of the composite scatterer made of such a rod and conformal strip of graphene when illuminated with an H-polarized plane wave. Our full-wave analysis is based on a hypersingular electric-field integral equation relatively to the current on the strip, discretized using the meshless Nystrom-type method, to guarantee the convergence of the obtained results. We present the reliefs of the normalized ACS and ECS as a function of the rod dielectric permittivity and the frequency for different graphene strip widths, in the range from 3 GHz to 60 GHz. At resonance frequencies in this range, we plot near field patterns. © 2020 IEEE.