20.500.12556/DKUM-61546 Povezana particijska dimenzija grafov Connected partition dimension of graphs Diplomsko delo obravnava povezano particijsko dimenzijo grafov. Tvorijo ga tri poglavja. V prvem poglavju so predstavljeni osnovni pojmi, definicije in primeri iz teorije grafov. Drugo poglavje je namenjeno predstavitvi povezane particijske dimenzije grafov in njenih lastnosti. Obravnavana je povezava med particijsko dimenzijo in povezano particijsko dimenzijo grafov. Podana je karakterizacija grafov reda n, katerih povezana particijska dimenzija je enaka 2, n ali n-1. V tretjem poglavju je določena povezana particijska dimenzija dreves, koles in Jahangirovih grafov. Poleg tega je dokazan izrek, ki pravi, da za vsak par celih števil a in b, kjer je a večje ali enako 3 in b manjše ali enako 2a-1 in hkrati večje od a, obstaja povezan graf G, da je pd(G)=a in cpd(G)=b. The diploma paper deals with the connected partition dimension of graphs. It consists of three chapters. The first chapter presents the basic concepts, definitions and examples from the graph theory. The second chapter presents connected partition dimension of graphs and its properties. It deals with the relationship between the partition dimension of graphs and the connected partition dimension of graphs. The characterization of graphs of order n, for which the connected partition dimension is equal to 2, n or n – 1 is given. In the third chapter, the connected partition dimension of trees, wheels and Jahangir graphs is determined. Moreover, the proof of the theorem which states that for every pair of integers a and b, with a greater than or equal to 3 and b less than or equal to 2a-1 and b greater than a, there is a connected graph G having pd(G)=a and cpd(G)=b is given. Rešljiva particija particijska dimenzija grafov povezana particijska dimenzija grafov drevesa kolesa Jahangrovi grafi. Resolving partition partition dimension of graphs connected partition dimension of graphs trees wheels Jahangir graphs. true true false [J. Slemenšek] Slovenski jezik Angleški jezik Diplomsko delo 2016-08-10 12:45:43 2016-09-23 13:16:00 2022-06-26 03:07:13 2019-07-11 12:24:54 2016 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17(043.2) 22572808 URN:SI:UM:DK:W7TTE7HG UN_Slemensek_Jasna_2016.pdf UN_Slemensek_Jasna_2016.pdf 1 AA20B23EB1C643B31003C665B520ECC4 c6bce030947c866dedd2fa86d7fa49d07adb2f5d788e5f258ea4db1277f6687d fd89dece-7c0c-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=98123 Fakulteta za naravoslovje in matematiko 0 0 0