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Problem stopnje in premera : diplomsko delo
Matjašič, Telopea
V 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, serious
Publication and manufacture - Maribor : [T. Matjašič], 2016
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