{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T12:50:54Z","timestamp":1648903854514},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:p> A semigraph, defined as a generalization of graph by Sampathkumar, allows an edge to have more than two vertices. The idea of multiple vertices on edges gives rise to multiplicity in every concept in the theory of graphs when generalized to semigraphs. <\/jats:p><jats:p> In this paper, we define a representing matrix of a semigraph [Formula: see text] and call it binomial incidence matrix of the semigraph [Formula: see text]. This matrix, which becomes the well-known incidence matrix when the semigraph is a graph, represents the semigraph uniquely, up to isomorphism. We characterize this matrix and derive some results on the rank of the matrix. We also show that a matrix derived from the binomial incidence matrix satisfies a result in graph theory which relates incidence matrix of a graph and adjacency matrix of its line graph. We extend the concept of \u201ctwin vertices\u201d in the theory of graphs to semigraph theory, and characterize them. Finally, we derive a systematic approach to show that the binomial incidence matrix of any semigraph on [Formula: see text] vertices can be obtained from the incidence matrix of the complete graph [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830921500178","type":"journal-article","created":{"date-parts":[[2020,9,3]],"date-time":"2020-09-03T10:27:55Z","timestamp":1599128875000},"page":"2150017","source":"Crossref","is-referenced-by-count":0,"title":["Binomial incidence matrix of a semigraph"],"prefix":"10.1142","volume":"13","author":[{"given":"Jyoti","family":"Shetty","sequence":"first","affiliation":[{"name":"Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka 576104, India"}]},{"given":"G.","family":"Sudhakara","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka 576104, India"}]}],"member":"219","published-online":{"date-parts":[[2020,10,20]]},"reference":[{"key":"S1793830921500178BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-6569-9"},{"key":"S1793830921500178BIB002","doi-asserted-by":"publisher","DOI":"10.1137\/1004057"},{"key":"S1793830921500178BIB003","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"S1793830921500178BIB004","volume-title":"Linear Algebra","author":"Hoffman K.","year":"2017","edition":"2"},{"issue":"5","key":"S1793830921500178BIB005","first-page":"898","volume":"3","author":"Murugesan N.","year":"2014","journal-title":"Int. J. Eng. Res. Technol."},{"key":"S1793830921500178BIB006","volume-title":"Semigraphs and Their Applications","author":"Sampathkumar E.","year":"2019"},{"issue":"1","key":"S1793830921500178BIB007","first-page":"7","volume":"27","author":"Ramaswamy H. N.","year":"2017","journal-title":"Adv. Studies Contemp. Math."},{"issue":"3","key":"S1793830921500178BIB008","first-page":"349","volume":"24","author":"Ramaswamy H. N.","year":"2014","journal-title":"Adv. Studies Contemp. Math."},{"key":"S1793830921500178BIB009","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2009","edition":"2"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500178","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,28]],"date-time":"2021-04-28T07:28:36Z","timestamp":1619594916000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500178"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,20]]},"references-count":9,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["10.1142\/S1793830921500178"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500178","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,20]]}}}