Projective dimension and regularity of the path ideal of the line graph
arXiv:1610.02958
Abstract
By generalizing the notion of the path ideal of a graph, we study some algebraic properties of some path ideals associated to a line graph. We show that the quotient ring of these ideals are always sequentially Cohen-Macaulay and also provide some exact formulas for the projective dimension and the regularity of these ideals. As some consequences, we give some exact formulas for the depth of these ideals.
arXiv commentarXiv admin note: text overlap with arXiv:0902.0902 by other authors