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Acta Mathematica Vietnamica

On the Index of Depth Stability of Symbolic Powers of Cover Ideals of Graphs

S. A. Seyed Fakhari , icon-email S. Yassemi

Abstract

Let G be a graph with n vertices and let S=K[x1,,xn] be the polynomial ring in n variables over a field K. Assume that I(G) and J(G) denote the edge ideal and the cover ideal of G, respectively. We provide a combinatorial upper bound for the index of depth stability of symbolic powers of J(G). As a consequence, we compute the depth of symbolic powers of cover ideals of fully clique-whiskered graphs. Meanwhile, we determine a class of graphs G with the property that the Castelnuovo–Mumford regularity of S/I(G) is equal to the induced matching number of G.