Monomial s-sequences arising from graph ideals

Ideals arising from graphs are investigated via -sequences theory. In particular, the notion of -sequence for the generators of the edge ideal () of a connected acyclic graph is considered in order to obtain a description of the Groebner basis for the relation ideal of the symmetric algebra of (). For ideals generated by an -sequence, we are able to compute certain standard algebraic invariants of their symmetric algebra in terms of the corresponding invariants of quotients of the polynomial ring related to such graphs. Being the initial ideal of well-determined with respect to a monomial order, it defines the edge ideals of supporting graphs to , more suitable for instance in the management of sensitive data.