Distancijsko regularni grafovi

master's thesis

• Title (english): Distance regular graphs
• Author: Kristina Škufca
• Mentor: Vedran Krčadinac (mentor)
• Committee member: Vedran Krčadinac (predsjednik povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Željka Milin Šipuš (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-03-04, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Tema ovog diplomskog rada su distancijsko regularni grafovi. Rad se sastoji od četiri poglavlja i dodatka. Nakon uvoda u teoriju grafova definirani su distancijsko regularni grafovi i dana su njihova osnovna svojstva. Navode se neki osnovni primjeri distancijsko regularnih grafova, te se obrađuju jako regularni grafovi koji su poseban slučaj kada je dijametar 2. U daljnjem razvoju teorije uvode se matrice te definicija distancijsko regularnih grafova preko njih. Dani su glavni iskazi, dokazi i rezultati vezani za distancijske matrice distancijsko regularnih grafova i njihove produkte. U zadnjem poglavlju uvode se asocijacijske sheme i njihovu povezanost s distancijsko regularnim grafovima. Navodi se i Bose-Mesnerova algebra te svi parametri vezani za asocijacijske sheme i kako su oni povezane sa presječnim brojevima distancijsko regularnih grafova. Za kraj se spominju P-polinomijalne sheme i njihovi najvažniji primjeri. U dodatku su navedeni mali primjeri distancijsko regularnih grafova i njihovi presječni nizovi.

Abstract (english)

The topic of this master thesis are distance regular graphs. The thesis is divided into four sections and an appendix. After an introduction to graph theory we define distance regular graphs and their main properties. We give some essential examples of distance regular graphs, and we elaborate strongly regular graphs, which are the special case of diameter 2. In further development of the theory we introduce matrices and give the definition of the distance regular graphs through them. We give some main statements, proofs and results regarding the distance matrices of the distance regular graphs and their products. In the last section we introduce association schemes and their relation to distance regular graphs. We mention the Bose-Mesner algebra and all the parameters related to association schemes and how they are connected with intersection numbers of distance regular graphs. Lastly, we mention P-polynomial schemes and two most important examples. The appendix contains a table of small distance regular graphs and their intersection arrays.

• Keywords: teorija grafova; jako regularni grafovi; distancijske matrice; Bose-Mesnerova algebra; asocijacijske sheme
• Keywords (english): graph theory; strongly regular graphs; distance matrices; Bose-Mesner algebra; association schemes
• Language: croatian
• URN:NBN: urn:nbn:hr:217:810981
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2023-03-31
• Created on: 2022-03-31 12:03:33