Comparing symbolic powers of edge ideals of weighted oriented graphs

نویسندگان

چکیده

Let $D$ be a weighted oriented graph and $I(D)$ its edge ideal. If contains an induced odd cycle of length $2n+1$, under certain condition we show that $ {I(D)}^{(n+1)} \neq {I(D)}^{n+1}$. We give necessary sufficient for the equality ordinary symbolic powers ideal having each in some it. characterize naturally unicyclic graphs with unique cycles even their ideals. D^{\prime} obtained from after replacing weights vertices non-trivial which are sinks, by trivial weights. $I(D^{\prime})$ behave similar way. Finally, if is any star graph, {I(D)}^{(s)} = {I(D)}^s all $s \geq 2.$

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ژورنال

عنوان ژورنال: Journal of Algebraic Combinatorics

سال: 2022

ISSN: ['0925-9899', '1572-9192']

DOI: https://doi.org/10.1007/s10801-022-01118-1