Regularity of symbolic powers of edge ideals of Cameron-Walker graphs

摘要

A Cameron-Walker graph is a graph for which the matching number and the induced matching number are the same. Assume that G is a Cameron-Walker graph with edge ideal I(G), and let ind-match (THORN) be the induced matching number of G. It is shown that for every integer s >= 1, we have the equality reg (I(G)((s)) = 2s + ind-match (G) - 1, where I(G)((s)) denotes the s-th symbolic power of I(G).