Abstract
In this paper, we will study the characterization of Cohen-Macaulayness of some edge-weighted graphs. For cycle and tree edge-weighted graph, we will reprove the characterization of Cohen-Macaulayness of an edge-weighted cycle and an edge-weighted tree due to C.Paulsen and Wagstaff (2013) [1]. Our proof used a criterion of Hochster for Cohen-Macaulayness of a monomial ideal [2].
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