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Let C be a clutter and let A be its incidence matrix. If the linear systemx>=0;xA<=1 has the integer rounding property, we give a description of thecanonical module and the a-invariant of certain normal subrings associated toC. If the clutter is a connected graph, we describe when the aforementionedlinear system has the integer rounding property in combinatorial and algebraicterms using graph theory and the theory of Rees algebras. As a consequence weshow that the extended Rees algebra of the edge ideal of a bipartite graph isGorenstein if and only if the graph is unmixed.

Systems with the integer rounding property in normal monomial subrings