NONE 20260108120829282 wseas/wseas content-registration-form+ja@crossref.org content-registration-form WSEAS TRANSACTIONS ON SYSTEMS 1109-2777 2224-2678 Abdur Rohman Department of Mathematical Sciences, Bodoland University, Kokrajhar, 783370, INDIA https://orcid.org/0009-0006-1353-6009 Surajit Kr. Nath Department of Mathematical Sciences, Bodoland University, Kokrajhar, 783370, INDIA https://orcid.org/0000-0002-2142-393X Semigraph represents a system where a relationship occurs between two or more than two objects/elements along with prescribed the condition. Threshold semigraph is a concept that deals with a system which involves certain weights on its edge/partial edge. The structure of threshold semigraph is a robust concept and can be used in many important mathematical models. Here, we have introduced threshold semigraph and some related results. An application of threshold semigraph related to the Product Distribution System (PDS) is also discussed here. 01 08 2026 01 08 2026 25 3 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/23202.2026.25.3 https://wseas.com/journals/systems/2026/a065102-001(2026).pdf M.C. Golumbic,“Algorithmic Graph Theory and Perfect Graphs”, Annals of Discrete Mathematics. M.C. Golumbic, “Tolerance Graphs”, Discrete Applied Mathematics 9(1984)157- 170. North-Holland. DOI: 10.1016/0166-218X(84)90016-7 DOI: 10.1016/0166-218X(84)90016-7 N.V.R. Mahadev, U.N.Peled, “Threshold Graphs and Related Topics”, Annals of Discrete Mathematics. E. Sampathkumar, “Semigraph and Their Applications”, Academy of Discrete Mathematics and Applications, India, 2000. S.K. Nath and P. Das, “Matching in Semigraph”,International Journal of Computer Application”,Vol 6, No. 3, 2013. S. Sonawane, P. Kulkarni, C. Deshpande, B. Athawale, “Extractive summarization using semigraph (ESSg)”, Evolving Systems, 10, 409-424, 2019. DOI: 10.1007/s12530-018-9246-8 DOI: 10.1007/s12530-018-9246-8 A. Rohman, S.K. Nath, S. Sonawane, “Formulation, Proposition and Application of Interval Semigraph”, WSEAS Transactions on Computer Research, Vol. 12, 264-268, 2024. https://doi.org/10.37394/232018.2024.12.25. DOI: 10.37394/232018.2024.12.25 DOI: 10.37394/232018.2024.12.25 A. Rohman, S.K. Nath, “Introduction to Tolerance Semigraph”, WSEAS Transactions on Mathematics, Vol. 22, 884-887, 2023. https://doi.org/10.37394/23206.2023.22.96. DOI: 10.37394/23206.2023.22.96 DOI: 10.37394/23206.2023.22.96 V. Chvatal and P.L. Hammer, Aggregation of inequalities in integer programming. In P.L.Hammer, E.L.Johnson, B.H.Korte, G.L. Nemhauser, editors, Studies in Interger Programming, pages 145-162. North-Holland, New York, 1977. Annals of Discrete Mathematics 1. DOI: 10.1016/S0167-5060(08)70731-3 DOI: 10.1016/S0167-5060(08)70731-3 V. Chvatal and P.L. Hammer, “Set-packing problems and threshold graphs”,University of Waterloo, Canada, August 1973.