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تسجيل مستخدم جديدRegularity of Symbolic Powers of Edge Ideals
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In this article, we prove that for several classes of graphs, the Castelnuovo-Mumford regularity of symbolic powers of their edge ideals coincide with that of their ordinary powers.
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In this article, we study the regularity of integral closure of powers of edge ideals. We obtain a lower bound for the regularity of integral closure of powers of edge ideals in terms of induced matching number of graphs. We prove that the regularity
of integral closure of powers of edge ideals of graphs with at most two odd cycles is the same as the regularity of their powers.
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Let $mathcal{D}$ be a weighted oriented graph and $I(mathcal{D})$ be its edge ideal. In this paper, we show that all the symbolic and ordinary powers of $I(mathcal{D})$ coincide when $mathcal{D}$ is a weighted oriented certain class of tree. Fi
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Let $G$ be a simple graph and $I$ its edge ideal. We prove that $${rm reg}(I^{(s)}) = {rm reg}(I^s)$$ for $s = 2,3$, where $I^{(s)}$ is the $s$-th symbolic power of $I$. As a consequence, we prove the following bounds begin{align*} {rm reg} I^{s} & l
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We compute the Betti numbers for all the powers of initial and final lexsegment edge ideals. For the powers of the edge ideal of an anti-$d-$path, we prove that they have linear quotients and we characterize the normally torsion-free ideals. We deter
mine a class of non-squarefree ideals, arising from some particular graphs, which are normally torsion-free.
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