O P - temenima nekih stabala

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O P - temenima nekih stabala

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dc.contributor.advisor Lipkovski, Aleksandar
dc.contributor.author Erić, Lj. Aleksandra
dc.date.accessioned 2013-03-04T09:16:52Z
dc.date.available 2013-03-04T09:16:52Z
dc.date.issued 2012
dc.identifier.uri http://hdl.handle.net/123456789/2488
dc.description.abstract This thesis concerns P-vertices and P-set of non-singular acyclic matrices A and also singular acyclic matrices. It was shown that each singular matrix of order n has at most n ¡ 2 P-vertices. Also, it is shown that this does not hold for non-singular acyclic matrices by constructing non-singular acyclic matrices whose graphs are T having n¡1 ( or n) P-vertices. These matrices also achieve maximum size of P-set over non-singular acyclic matrices whose graphs are T. In this thesis, there is classi¯cation of the trees for which there is non- singular matrix where each vertex is P-vertex. In particular, it is shown that such trees have an even number of vertices. Both results provide answer to questions proposed by I.-J. Kim and B. L. Shader. In the end, related classi¯cations on non-singular trees with the size of a P-set bounded are addressed. Also, it is shown that double star DSn with n vertices, is an example of a tree such that, for each non-singular matrix A whose graph is DSn the number of P-vertices of A is less than n¡2. This example provides a positive answer to a question proposed recently by Kim and Shader. A recent classi¯cation of those trees for which each of associated acyclic matrices has distinct eigenvalues whenever the diagonal entries are distinct was established. Here is analyze of maximum number of distinct diagonal entries, and corresponding location, in order to preserve that multiplicity characterization. Recently, the multiplicities of eigenvalues of ©-binary tree was analyzed. This paper carry this discussion forward extending their results to larger family of trees, namely, the wide double path, a tree consisting of two paths that are joined by another path. Some introductory considerations for dumbbell graphs are mentioned re- garding the maximum multiplicity of the eigenvalues. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2013-03-04T09:16:52Z No. of bitstreams: 1 Eric_Aleksandra.pdf: 2125180 bytes, checksum: 8ad0f234e5facd78da148357a65d2e97 (MD5) en
dc.description.provenance Made available in DSpace on 2013-03-04T09:16:52Z (GMT). No. of bitstreams: 1 Eric_Aleksandra.pdf: 2125180 bytes, checksum: 8ad0f234e5facd78da148357a65d2e97 (MD5) Previous issue date: 2012 en
dc.language.iso sr en_US
dc.publisher Belgrade en_US
dc.title O P - temenima nekih stabala en_US
mf.author.birth-date 1967
mf.author.birth-place Belgrade
mf.author.birth-country Serbia
mf.subject.area Mathematics en_US
mf.subject.keywords graph, acyclic matrix, eigenvalue, multiplicity, P-vertex, P-set, en_US
mf.subject.keywords tree, double star. en_US
mf.subject.subarea Algebra en_US
mf.contributor.committee da Fonseca, Carlos Martins
mf.contributor.committee Kalajdžić, Gojko
mf.contributor.committee Čukić, Ljubomir
mf.university.faculty Mathematical en_US
mf.document.references 26 en_US
mf.document.pages 62 en_US
mf.document.location Belgrade en_US
mf.document.genealogy-project No en_US
mf.university Belgrade en_US

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