  Reflexive polytopes form one of the distinguished classes of lattice
polytopes. Especially reflexive polytopes which possess the integer
decomposition property are of interest. In the present paper, by virtue of the
algebraic technique on Gr\"onbner bases, a new class of reflexive polytopes
which possess the integer decomposition property and which arise from perfect
graphs will be presented. Furthermore, the Ehrhart $\delta$-polynomials of
these polytopes will be studied.
