20.500.12556/RUL-120182 Kombinatorična teorija matrik delo diplomskega seminarja Combinatorial matrix thoery Delo opisuje nekatere osnovne rezultate kombinatorične teorije matrik. Kombinatorična teorija matrik je veja matematike, ki združuje kombinatoriko, teorijo grafov in linearno algebro. V prvem delu diplomske naloge si podrobneje ogledamo algebraične lastnosti (0, 1)-matrik. Klasičen problem tlakovanja pravokotnikov zapišemo z matrično enačbo in s pomočjo lastnosti (0, 1)-matrik rešimo zanimiv kombinatorični primer. V drugem delu diplomske naloge graf predstavimo z matriko sosednosti ter incidenčno matriko. Izpeljemo povezavo med tema dvema matrikama in definiramo Laplaceovo matriko grafa. Povežemo nekatere lastnosti grafa z algebraičnimi lastnostmi matrike sosednosti ter incidenčne matrike. Na koncu se podrobneje posvetimo Laplaceovi matriki grafa in izpeljemo formulo za izračun števila vpetih dreves v grafu. This thesis describes some of the basic results of combinatorial matrix theory. Combinatorial matrix theory is a branch of mathematics that connects combinatorics, graph theory and linear algebra. The first part of the thesis deals with algebraic properties of (0, 1)-matrices. We reformulate an elementary problem in geometry in terms of matrices and solve an interesting combinatorial problem with the help of the properties of (0, 1)-matrices. In the second part of the thesis we represent a graph with its adjacency matrix and its incidence matrix. We derive a relation between the two matrices and define a Laplacian matrix of a graph. We connect properties of a graph with algebraic properties of its adjacency and incidence matrix. At the and we discuss Laplacian matrix of a graph and derive a formula for calculating the number of spanning trees in a graph. (0 1)-matrika matrika sosednosti spekter grafa incidenčna matrika Laplaceova matrika kompleksnost grafa (0 1)-matrix adjacency matrix graph spectrum incidence matrix Laplacian matrix graph complexity true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2020-09-17 07:16:34 2020-09-17 07:16:36 2024-05-29 14:36:47 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.64 110224 58842371 1469.pdf 1469.pdf 1 4644E5E5D26869593039F8F135462FC6 ee0b2a086ff53ed349299ed32e0717e2a982defd6343bab41224348bf1bf1e0c 05525568-a1ba-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=134962 Fakulteta za matematiko in fiziko 0 0 0