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Let C be a clutter and let A be its incidence matrix. If the linear system x > 0; x A < 1 has the integer rounding property, we give a description of the canonical module and the a-invariant of certain normal subrings associated to C. If the clutter is a connected graph, we describe when the aforementioned linear system has the integer rounding property in combinatorial and algebraic terms using graph theory and the theory of Rees algebras. As a consequence we show that the extended Reesdoi:10.1590/s0001-37652010000400002 fatcat:neezvcqy6fhxdlcnsu25n7k7sy