IRREDUCIBLE DECOMPOSITION OF SQUARE OF EDGE IDEALS

Abstract

Let R = K[x 1,...,x d] be the polynomial ring in d variables over K, G = (V(G),E(G)) a graph associated with variables {x 1,...,x d } and IG an edge ideal. In this paper, we describe the structure of irreducible decompositions of square of edge ideals IG2 of the polynomial ring via corner elements and coclique sets.