Miklošič Library FPNM, Maribor (PEFMB)
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Problem stopnje in premera : diplomsko deloMatjašič, TelopeaV diplomskem delu je obravnavan problem stopnje in premera. Poiskati hočemo največji graf, glede na število njegovih vozlišč, ki bo imel premer $k geq 1$ in največjo stopnjo vozlišč $d geq 1$. ... Število vozlišč takšnega grafa je navzgor omejeno z Mooreovo mejo: $1 + d sum_{i=0}^{k-1}(d-1)^i$. Graf, ki doseže to mejo, imenujemo Mooreov graf. Izkaže se, da je zelo malo grafov, ki dosežejo to mejo, zato se je smiselno osredotočiti na grafe, katerih število vozlišč je blizu tej meji. Iskanje teh grafov poteka na dva načina. Najprej pogledamo kako so z dokazi o neobstoju grafov zniževali zgornjo mejo, nato pa predstavimo nekatere splošne metode s katerimi so izboljševali spodnjo mejo in se na ta način približali Mooreovi meji. Ugotovimo, da je do sedaj znanih le malo grafov, ki so optimalne velikosti oziroma, ki odgovorijo na naš zastavljen problem. Posebej opišemo grafe, za katere je premer bodisi 2 bodisi 3.Type of material - undergraduate thesis ; adult, seriousPublication and manufacture - Maribor : [T. Matjašič], 2016Language - slovenianCOBISS.SI-ID - 22476552
Author
Matjašič, Telopea
Other authors
Jakovac, Marko
Topics
Univerzitetna in visokošolska dela |
diplomska dela |
teorija grafov |
stopnja |
premer |
Mooreov graf |
Mooreova meja |
theses |
graph theory |
degree |
diameter |
Moore graph |
Moore bound
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M DIPL 0000000051 MATJAŠIČ T. Problem IN: 920160084 M DIPL 51 MATJAŠIČ T. Problem IN: 920160084 |
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JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
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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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Matjašič, Telopea | ![]() |
Jakovac, Marko | 29919 |
Source: Personal bibliographies
and: SICRIS
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