27c5da03-973f-429b-b76c-f7bbd6f335eb20230710082659339naun:naunmdt@crossref.orgMDT DepositInternational Journal of Pure Mathematics2313-057110.46300/91019http://www.naun.org/cms.action?id=6985411202341120231010.46300/91019.2023.10https://npublications.com/journals/puremath/2023.phpOn Minimum Covering Energy of SemigraphArdhendu KumarNandiDepartment of Mathematics, Basugaon College, Basugaon, 783372, IndiaSurajit Kr.NathDepartment of Mathematical Sciences, Bodoland University, Kokrajhar, 783370, IndiaNiva RaniNathDepartment of Mathematical Sciences, Bodoland University, Kokrajhar, 783370, IndiaA compromise between the concept of graph and hypergraph is semigraph. This paper introduced the concept of minimum covering matrix and minimum covering energy of a semigraph G. The minimum covering energy is the summation of singular values of the minimum covering matrix. Upper and lower bounds for minimum covering energy are established and also derive some relationship between minimum covering energy and energy of semigraph G.7102023710202328324https://npublications.com/journals/puremath/2023/a082019-004(2023).pdf10.46300/91019.2023.10.4https://npublications.com/journals/puremath/2023/a082019-004(2023).pdfI Gutman, “The energy of a graph”, Ber.Math. Statist Sekt. Forshungsz. Graz, 103, pp. 1-22, 1978. C. Adiga, E. Sampathkumar, M. A. Sriraj and A. S. Shrikanth, “Color energy of a graph”, Proc. Jangjeon Math. Soc., 16 (3), pp. 335-351, 2013. P. B. Joshi and M. Joseph, “Further results on color energy of graphs”, Acta Univ. Sapientiae Inform., 9 (2), pp. 119-131, 2017. G. Indulal, I. Gutman And A. Vijayakumar, “On distance energy of graphs”, Match communications in Mathematical and in Computer Chemistry, 60, pp. 461- 472, 2008. C. Adiga, A. Bayad, I Gutman and S A Srinivas, “The minimum covering energy of a graph”, Kragujevac J. Sci., 34, pp. 39-56, 2012. E. Sampatkumar, “Semigraphs and their Applications”, Academy of Discrete Mathematics and Application, 2019, India, 10.1016/j.akcej.2018.06.006Y. S. Gaidhani, C. M. Deshpande and S Pirzada, “Energy of a semigraph”, AKCE International Journal of graphs and Combinatorics, 16, pp. 41-49, 2019. S. K. Nath, I. Gutman and A. K. Nandi, “Distance Matrix and Energy of Semigraph”, Bull. Int. Math. Virtual Inst., 11 (3), pp.597-603, 2021. 10.1016/j.endm.2017.11.037Y. S. Gaidhani, C. M. Deshpande, and B. P. Athawale, “Adjacency Matrix of a Semigraphs”, Electronic Notes Disc. Math., 63, pp. 399-406, 2017. V. Nikiforov, “The energy of graphs and matrices”, J. Math. Anal. Appl., 326, pp. 1472-1475, 2007. I. Gutman and O. E. Polansky, “Mathematical Concepts in Organic Chemistry”, Springer, Berlin, 1986. 10.17654/dm02702019S. K. Nath and A. K. Nandi, “Adjacency matrix of signed semigraph”, Adv. Appl. Discrete Math., 27 (2), pp. 193-207, 2021.