Faculty of Education, Lj. (PEFLJ)
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Indeks razdaljne neuravnoteženosti grafov [Elektronski vir] = Distance-unbalancedness index of graphs : magistrsko deloUranič, NušaV magistrskem delu najprej predstavimo pojem razdaljno uravnoteženega grafa ter si pogledamo nekaj primerov takih grafov in primer družine grafov, kjer noben član ni razdaljno uravnotežen. Nato ... predstavimo naravno posplošitev tega koncepta ter tako pridemo do l-razdaljno uravnoteženih grafov. Tu si za primer najprej pogledamo Cayleyeve grafe Abelovih grup, ki so povsem razdaljno uravnoteženi, nato pa se osredotočimo na posplošene Petersenove grafe. V nadaljevanju pridemo preko tako imenovanega Mostarjevega indeksa do indeksa razdaljne neuravnoteženosti ter določimo vrednosti tega indeksa za poti in polne večdelne grafe ter nato še za dve manj znani družini grafov. Da so navedene vrednosti pravilne, tudi teoretično dokažemo. Zatem predstavimo nekaj rezultatov in domnev glede najmanjšega in drugega najmanjšega možnega indeksa razdaljne neuravnoteženosti za drevesa danega reda. Za konec predstavimo dokaz izreka, ki nam pove, da je med vsemi drevesi reda n, kjer je n>=5, zvezda S_{n-1} edino drevo reda n z najmanjšim možnim indeksom razdaljne neuravnoteženosti.Type of material - master's thesis ; adult, seriousPublication and manufacture - [N. Uranič], 2024 ; LjubljanaLanguage - slovenianCOBISS.SI-ID - 199563267
Author
Uranič, Nuša
Other authors
Šparl, Primož
Topics
Matematika |
Univerzitetna in visokošolska dela |
l-razdaljno uravnotežen graf |
indeks razdaljne neuravnoteženosti |
drevo |
l-distance-balanced graph |
distance-unbalancedness index |
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Database name | Field | Year |
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Uranič, Nuša | ![]() |
Šparl, Primož | 23341 |
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