Algebraična teorija grafov z aplikacijami / Algebraic Graph Theory with Applications
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Naziv Tittle |
Algebraična teorija grafov z aplikacijami / Algebraic Graph Theory with Applications |
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Akronim Acronim |
J1-6720 |
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Opis Description |
(SI) Predlagani projekt je naravno nadaljevanje temeljnega raziskovalnega projekta J1-4021 "Algebraična teorija grafov in aplikacije", ki ga vodi Dragan Marušič in se zaključuje v mesecu juniju 2014 s pridobitvijo velikega števila novih pomembnih rezultatov na tem področju. Osredotočen je na najbolj obetavne raziskovalne smeri znotraj ATG: krovne tehnike, konstrukcije katalogov; študij reprezentacije tranzitivnih grup na lastnih podprostorih matrike sosednosti danega grafa; konstrukcija (usmerjenih) krepko regularnih grafov, ki premorejo predpisane simetrijske lastnosti; študij določenega tipa dvodelnih razdaljno-regularnih grafov; študij grafov, ki premorejo določena grupna delovanja, kot so: grafi, ki premorejo ločno tranzitivno grupo avtomorfizmov z ne-pol-regularno abelovo podgrupo edinko, k-pretoki v grafih, ki premorejo točkovno tranzitivno grupno delovanje, grafi, ki premorejo dolge konsistentne cikle; ne-schurovi S-kolobarji, ki so vezni člen med abstraktno teorijo grup in algebraično kombinatoriko in problem ločljivosti S-kolobarjev nad cikličnimi grupami skupaj z uporabo v AGT in končni geometriji; ter študij korespondence med AGT in kriptologijo. (EN) This project proposal is a natural follow-up of the basic research project J1-4021 Algebraic Graph Theory and Applications (2011-2014) led by Dragan Marušič, which is going to end in June 2014 with many important new contributions to the field. It concentrates on some of the most relevant research areas within AGT: Covering techniques, construction of catalogues, and algorithmic aspects; the study of representations of transitive groups on eigenspaces of the adjacency matrix of a given graph; the construction of (directed) strongly regular graphs admitting particular symmetry properties; the study of a certain type of bipartite distance-regular graphs; the study of graphs admitting particular group actions, such as graphs admitting an arc-transitive group of automorphisms with a non-semi-regular abelian normal subgroup, k-flows in graphs admitting vertex-transitive group actions, graphs admitting long consistent cycles; non-schurian S-rings which form a link between the abstract group theory and algebraic combinatorics, and the separability problem of S-rings over cyclic groups together with applications to AGT and finite geometry; and the study of the correspondence between AGT and cryptology. |
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Vrsta projekta Project Type |
Temeljni projekt |
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Trajanje Duration |
01/07/2014 - 30/06/2017 |
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URL URL |
https://www.sicris.si/public/jqm/search_basic.aspx?lang=slv&opdescr=search&opt=2&subopt=1&code1=cmn&code2=auto&search_term=J1-6720 |
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Vodja projekta Project Leader |
Dragan Marušič |
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Sodelujoče organizacije Participating organizations |
UP FAMNIT; UL Pedagoška fakulteta |
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Oddelek Department |
Oddelek za matematiko IAM |