Let S=Kx₁, , xₙ denote the polynomial ring in n variables over a field K and I S a monomial ideal. Given a vector cⁿ, the ideal I₂ is the ideal generated by those monomials belonging to I whose exponent vectors are componentwise bounded above by c. Let ₂ (I) be the largest integer q for which (Iq) ₂ 0. For a finite graph G, its edge ideal is denoted by I (G). Let B (c, G) be the toric ring which is generated by the monomials belonging to the minimal system of monomial generators of (I (G) ^₂ (I) ) ₂. In a previous work, the authors proved that (I (G) ^₂ (I) ) ₂ is a polymatroidal ideal. It follows that B (c, G) is a normal Cohen--Macaulay domain. In this paper, we study the Gorenstein property of B (c, G).
Hibi et al. (Wed,) studied this question.