$t$-clique ideal and $t$-independence ideal of a graph
Commutative Algebra
2017-12-05 v1
Abstract
In this paper, we introduce and study families of squarefree monomial ideals called clique ideals and independence ideals that can be associated to a finite graph. A family of clique ideals with linear resolutions has been characterized. Moreover some families of graphs for which the quotient ring of their clique ideal is Cohen-Macaulay are introduced and some homological invariants of the clique ideal of a graph which is the complement of a path graph or a cycle graph, are obtained. Also some algebraic properties of the independence ideal of path graphs, cycle graphs and chordal graphs are studied.
Keywords
Cite
@article{arxiv.1712.00583,
title = {$t$-clique ideal and $t$-independence ideal of a graph},
author = {Somayeh Moradi},
journal= {arXiv preprint arXiv:1712.00583},
year = {2017}
}
Comments
to appear in "Communications in Algebra"