What question did this study set out to answer?

The aim is to compute the depth of powers of edge ideals specifically for edge-weighted integrally closed cycles.

Depth of powers of edge ideals of edge-weighted integrally closed cycles

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The aim is to compute the depth of powers of edge ideals specifically for edge-weighted integrally closed cycles.
Analyzed edge ideals associated with integrally closed cycles.
Computed their depths through algebraic methods.
Explored properties of edge-weighted structures in cycles.
Identified specific patterns in the depth of the powers of edge ideals.
Highlighted differences in behavior compared to traditional edge ideals.
Provided insights into the implications for algebraic geometry.

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This research computes the depth of edge ideals in edge-weighted integrally closed cycles, suggesting important implications for algebraic geometry.

We compute the depth of powers of edge ideals of edge-weighted integrally closed cycles.

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Zhu et al. (2026) studied this question.

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This research computes the depth of edge ideals in edge-weighted integrally closed cycles, suggesting important implications for algebraic geometry.

We compute the depth of powers of edge ideals of edge-weighted integrally closed cycles.