Algebraic Properties of Edge Ideals and Cover Ideals of Unbalanced Crown Graphs
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DOI: 10.1007/s41980-021-00560-4
Abstract: In this paper, we introduce the unbalanced crown graphs $${\mathcal {C}}_{m,n}$$ , and compute all graded Betti numbers of edge ideals of these graphs in terms of associated numerical data. As a consequence, we determine… read more here.
Keywords: edge ideals; crown graphs; algebraic properties; unbalanced crown ... See more keywords
ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS
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DOI: 10.1017/nmj.2020.27
Abstract: Abstract Assume that G is a graph with edge ideal $I(G)$ and star packing number $\alpha _2(G)$ . We denote the sth symbolic power of $I(G)$ by $I(G)^{(s)}$ . It is shown that the inequality… read more here.
Keywords: edge ideals; symbolic powers; powers edge; ideals graphs ... See more keywords
Betti numbers of edge ideals of some graphs with application to graphs assigned to groups
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DOI: 10.2298/fil2406185r
Abstract: The article presents the Betti numbers of multiple complete split-like graphs, clique stars and their generalization. As an applications, we also give the Betti numbers of the graphs defined on groups, like power graphs of… read more here.
Keywords: betti numbers; edge ideals; ideals graphs; graphs application ... See more keywords