We study the scattering and absorption of the H-polarized plane wave by a dielectric tube with a graphene cover in the THz range. The tube is assumed to have circular cross-section. The analytical solution of the wave-scattering problem is based on the Maxwell equations and using the separation of variables in the polar coordinates. We assume the resistive boundary conditions on the zero-thickness graphene cover, where the graphene electron conductivity is included as a parameter and determined from the Kubo formalism.

The computed spectra of the total scattering cross-section and absorption cross-section display two different types of resonances: the localized-surface-plasmon (LSP) resonances of the graphene shell and resonances on conventional modes of a dielectric tube. The computed data can be useful for the design of graphene-based sensors of the changes in refractive index of host medium. For this purpose, the sensitivities and the figure-of-merit values of the LSP resonances are computed.