Regularity in weighted oriented graphs

Mandal, Mousumi; Pradhan, Dipak Kumar

doi:10.1007/s13226-021-00039-2

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2021

2024

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Cited by 4 publications

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“…Furthermore, algebraic invariants and properties like Cohen-Macaulayness and unmixedness of edge ideals of weighted oriented graphs have been studied in [9], [14], [19] and [20]. Recently regularity and projective dimension of the edge ideals of some classes of weighted oriented graphs have been studied in [3], [17], [23] and [24]. In [19], Y. Pitones et al have described the irreducible decomposition of I(D) for any weighted oriented graph D using the concept of strong vertex cover.…”

Section: Introuductionmentioning

confidence: 99%

Comparing symbolic powers of edge ideals of weighted oriented graphs

Mandal,

Pradhan

2021

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Let D be a weighted oriented graph and I(D) be its edge ideal. We give necessary and sufficient condition for the equality of ordinary and symbolic powers of edge ideals of certain classes of weighted oriented graphs. Let D ′ be the weighted oriented graph obtained from D after replacing the weights of vertices with non-trivial weights which are sink, by trivial weights. We show that symbolic powers of I(D) and I(D ′ ) behave in a similar way. Finally, if D is any weighted oriented star graph or some specific weighted naturally oriented path, we show that I(D) (s) = I(D) s for all s ≥ 2.

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