Narrow Results

This paper presents a complete characterization of an edge-weighted simple graph $G_{\omega }$, whose edge ideal $I(G_{\omega })$ is integrally closed. Furthermore, it is demonstrated that if $I(G_{\omega })$ is integrally closed and $G_{\omega }$ is an edge-weighted star graph, path, or cycle, then $I(G_{\omega })$ is normal.

This paper gives exact formulas for the regularity of powers of the edge ideal of an edge-weighted integrally closed cycle.