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arXiv · 1712.00583

$t$-clique ideal and $t$-independence ideal of a graph

Somayeh Moradi
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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 $G$ 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.

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Somayeh Moradi. 2017-12-02. $t$-clique ideal and $t$-independence ideal of a graph. https://arxiv.org/abs/1712.00583

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