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Posplošitve medianskih grafov : magistrsko deloTepeh, AleksandraMagistrsko delo obravnava medianske grafe in nekatere njihove posplOŠitve: kvazimedianske grafe, psevdomedianske grafe, šibko medianske grafe, grafe zastraženih inverzov in absolutno C-medianske ... grafe. Največjo pozornost namenjamo njihovi strukturi, ki jo odražajo t.i. amalgamacijski in ekspanzijski izreki, obravnavamo pa tudi izreke o fiksnih škatlah. Osnovni pojmi, med njimi najpomembnejši (zastražene množice, ekspanzije in amalgamacije), so predstavljeni v uvodnem poglavju. Spoznamo razred šibko modulamih g,1:afov, saj lahko nekatere obravnavane razrede grafov opišemo kot šibko modularne grafe brez prepovedanih induciranih podgrafov . V nadaljevanjuje vsakemu izmed zgoraj omenjenih razredov grafov namenjeno posebno poglavje. Ena izmed naj širših posplošitev je razred grafov zastraženih inverzov, ki jim posvetimo šesto poglavje. Karakteriziramo jih kotgrafe, ki jih lahko dobimo iz grafa KI z zaporedjem zastraženih ekspanzij glede na elementarne grafe ter kot grafe, ki jih lahko dobimo iz kartezičnih produktov elementarnih grafov z zaporedjem zastraženih amalgamacij. Dokažemo, da vsak graf zastraženih inverzov premore kot podgraf neko elementamo škatlo, ki je invariantna za vse njegove avtomorfizme. Iz omenjenih izrekov analogne izreke izpeljemo za podrazrede grafov zastraženih inverzov, zato se v predhodnih poglavjih osredotočamo na elementarne grafe posameznih razredov. Drugo poglavje je posvečeno medianskim, tretje kvazimedianskim, _četrto psevdomedianskim in peto šibko me<fianskim grafom. Absolutno C-medianski grafipredstavljajo drugo izmed obsežnih posplošitev medianskih grafov. V sedmem poglavju tako spoznamo zastraženostno imprint funkcijo in izreke o fiksnih škatlah; med drugim dokažemo, da vsak absolutno Cmedianski graf vsebuje zastraženo škatlo, ki je invariantna za vsak avtomorfizem tega grafa. V zaključku povzamemo najpomembnejše rezultate in nakažemo nadaljnje možnosti za raziskovanje.Type of material - master's thesis ; adult, seriousPublication and manufacture - Maribor : [A. Tepeh Horvat], 2005Language - slovenianCOBISS.SI-ID - 13866760
Author
Tepeh, Aleksandra
Other authors
Brešar, Boštjan
Topics
matematika |
teorija grafov |
medianski grafi |
ekspanzija |
amalgamacija |
magistrska dela |
mathematics |
graph theory |
median graphs |
expansion |
amalgamation
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Library/institution |
City | Acronym | For loan | Other holdings |
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Miklošič Library FPNM, Maribor | Maribor | PEFMB |
reading room 1 cop.
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National and University Library, Ljubljana | Ljubljana | NUK |
reading room 1 cop.
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University of Maribor Library | Maribor | UKM |
reading room 1 cop.
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Tepeh, Aleksandra | 23904 |
Brešar, Boštjan | 17005 |
Source: Personal bibliographies
and: SICRIS
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