Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/2049
Full metadata record
DC FieldValueLanguage
dc.contributor.authorZAFAR, SOHAIL-
dc.date.accessioned2017-12-11T06:01:08Z-
dc.date.available2017-12-11T06:01:08Z-
dc.date.issued2008-
dc.identifier.uri http://prr.hec.gov.pk/jspui/handle/123456789//2049-
dc.description.abstractLet J G denote the binomial edge ideal of a connected undirected graph G on n vertices. This is the ideal generated by the binomials x i y j −x j y i , 1 ≤ i < j ≤ n, in the polynomial ring S = K[x 1 , . . . , x n , y 1 , . . . , y n ] where {i, j} is an edge of G. Our aim in this thesis is to compute certain algebraic invariants like dimension, depth, system of parameters, regular sequence, Hilbert series and multiplicity of J G of some particular classes of binomial edge ideals of graphs. A large amount of information of an ideal is carried by its minimal free resolution. So we give information on the minimal free resolution on certain binomial edge ideals. We also give a complete description of the structure of the modules of deficiencies of binomial edge ideals of some classes of graphs. A generalization of the concept of a Cohen-Macaulay ring was introduced by S. Goto [7] under the name approximately Cohen-Macaulay. In this thesis we collect a few graphs G such that the associated ring S/J G is approximately Cohen-Macaulay. We also characterize all the trees that are approximately Cohen-Macaulay. As more generalized notion than approximately Cohen-Macaulay we also study se- quentially Cohen-Macaulay property for binomial edge ideals. We give a nice con- struction principle in this topic. ̃ on n vertices has the property that S/J ̃ is a Cohen-Macaulay The complete graph G G domain with a 1-linear resolution. As one of the main results we clarify the structure of S/J K m,n , where K m,n denotes the complete bipartite graph.en_US
dc.description.sponsorshipHigher Education Commission, Pakistanen_US
dc.language.isoenen_US
dc.publisherGC University Lahore, Pakistanen_US
dc.subjectNatural Sciencesen_US
dc.subjectMathematicsen_US
dc.subjectGeneral principles of mathematicsen_US
dc.subjectAlgebraen_US
dc.subjectArithmeticen_US
dc.subjectTopologyen_US
dc.subjectAnalysisen_US
dc.subjectGeometryen_US
dc.subjectNumerical analysisen_US
dc.subjectProbabilities & applied mathematicsen_US
dc.titleCombinatorial and Arithmetic Study of Binomial Edge Idealen_US
dc.typeThesisen_US
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

Files in This Item:
File Description SizeFormat 
1703S.pdfComplete Thesis472.09 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.