Invariants of the symbolic powers of edge ideals

摘要

Let G be a graph and I = 1(0) be its edge ideal. When G is the clique sum of two different length odd cycles joined at single vertex then we give an explicit description of the symbolic powers of I and compute the Waldschmidt constant. When C, is complete graph then we describe the generators of the symbolic powers of I and compute the Waldschmidt constant and the resurgence of I. Moreover for complete graph we prove that the Castelnuovo-Mumford regularity of the symbolic powers and ordinary powers of the edge ideal coincide.