Regularity in weighted oriented graphs

Mousumi Mandal () and Dipak Kumar Pradhan ()
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Mousumi Mandal: Indian Institute of Technology
Dipak Kumar Pradhan: Indian Institute of Technology

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 4, 1055-1071

Abstract: Abstract Let D be a weighted oriented graph with the underlying graph G and I(D), I(G) be the edge ideals corresponding to D and G respectively. We show that the regularity of edge ideal of a certain class of weighted oriented graph remains same even after adding certain kind of new edges to it. We also establish the relationship between the regularity of edge ideal of weighted oriented path and cycle with the regularity of edge ideal of their underlying graph when vertices of $$V^+$$ V + are sinks.

Keywords: Weighted oriented graph; labeled hypergraph; edge ideal; Castelnuovo-Mumford regularity; 13D02; 13F20; 13C10; 05C22; 05E40; 05C20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00039-2

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