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Algebraic study reveals irreducible decompositions and regularity bounds in k-edge weighted VEW graphs, advancing the classification of graph-based monomial ideals.
Let D be a k-edge weighted VEW graph and I = I (D) be its edge ideal. In this paper, we characterize the irredundant irreducible decomposition of edge ideal I. Also, we study the Cohen-Macaulay property and Castelnuovo-Mumford regularity of different classes of k-edge weighted VEW graphs.
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Kumar et al. (2026) studied this question.
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