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