20.500.12556/DKUM-21063 PALIČNO ŠTEVILO GRAFA GRAPH PEGGING NUMBER Diplomsko nalogo tvori šest poglavij. Po uvodu sledi poglavje z osnovnimi pojmi teorije grafov, ki so uporabljeni v diplomski nalogi. V drugem poglavju so predstavljene osnovne lastnosti igre s palicami ter definirani pojmi palično število, optimalno palično število, palična poteza, dvopalična poteza, odstranitvena poteza, razporeditev na grafu, dobra (multi) razporeditev na grafu, cilj poteze in izid razporeditve. V tretjem poglavju sta podana palično in optimalno palično število poti, ciklov in spojev grafov. Prikazani so tudi primeri razporeditve za nekatere poti in cikle manjšega reda. V četrtem poglavju sta podani palično in optimalno palično število kartezičnega produkta polnih grafov ter določeni spodnja in zgornja meja paličnega števila kartezičnega produkta $G \square K_n$, ki temelji na dvopaličnem številu. V petem poglavju je določeno palično število hiperkock. Poleg tega sta določeni še spodnja in zgornja meja za optimalno palično število hiperkock. V šestem poglavju pa so določene spodnje in zgornje meje za palično in optimalno palično število grafov z majhnim premerom. The graduation thesis consists of six sections. After introduction the basic concepts of the Graph Theory used in the thesis are presented. In the second section the basic properties of pegging are introduced and the definitions of pegging number, optimal pegging number, pegging move, pebbling move, removal move, distribution on a graph, proper(multi) distribution on a graph, target vertex and reach of a distribution are given. In the third section the pegging and the optimal pegging number of paths, cycles and joins are given and some examples of distributions for paths and cycles of small order are presented. In the fourth section the pegging and the optimal pegging number of the Cartesian product of complete graphs are determined. Moreover, the lower and the upper bound for the pegging number of the Cartesian product $G \square K_n$, which are based on the pebbling number, are established. In the fifth section the pegging number of the hypercubes and also the lower and the upper bound for the optimal pegging number of the hypercubes are determined. In the sixth section the lower and the upper bound for the pegging and the optimal pegging number of graphs of small diameter are presented. teorija grafov igre na grafih igra s palicami palično število grafa graph theory games on graphs graph pegging pegging number true true false [B. Mikelj] Slovenski jezik Angleški jezik Diplomsko delo 2011-10-20 20:46:59 2011-11-09 13:41:42 2022-04-14 08:30:23 2023-12-28 03:12:40 2011 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18751752 URN:SI:UM:DK:3YFHUO2X UNI_Mikelj_Barbara_2011.pdf UNI_Mikelj_Barbara_2011.pdf 1 3EF6922AA4EB569EACFCB765B041488D 2b596ab932bafeaf5d21fcedc2943b800cd71b8da6f52870859e004bf2a700bb c5df163e-7c05-11eb-bb7a-00155d0001ca 20.500.12556/dkum/16bfa6d1-9a65-4008-a3ed-ac5a6309db82 https://dk.um.si/Dokument.php?lang=slv&id=26483 Fakulteta za naravoslovje in matematiko 0 0 0