Edge ideals and connection problems

Abstract

Ideals arising from graphs are investigated via Grobner bases theory in order to introduce algebraic objects useful for applications related to the field of security. In particular, the notion of s-sequence for the generators of the edge ideal I(G) of any graph G is considered, so that a description of the Grobner basis for the relation ideal J of the symmetric algebra of I(G) can be obtained. Based on this approach, the initial ideal of J with respect to a monomial order is well-determined and defines the edge ideal of a supporting graph F, essential in transmitting.