Grafi z enolično [gamma]-množico

na magistrskem študijskem programu Izobraževalna matematika - enopredmetna

Darina Cvetrežnik (Author), Tanja Gologranc (Mentor)

Abstract

V magistrskem delu podrobneje obravnavamo grafe z enolično ▫$γ$▫-množico oziroma ▫$γ$▫-enolične grafe. To so grafi, ki imajo natanko eno najmanjšo dominantno množico. Sprva zapišemo nekaj osnovnih definicij in trditev o grafih, nato posebej obravnavamo dve družini grafov, in sicer drevesa ter bločne grafe. Podrobneje opišemo dominantno množico in dominantno število grafa. Dokažemo nekaj potrebnih in nekaj zadostnih pogojev za grafe z natanko eno ▫$γ$▫-množico. Nato se osredotočimo na drevesa. Predstavimo dve karakterizaciji ▫$γ$▫-enoličnih dreves ter obe karakterizaciji posplošimo na ▫$γ$▫-enolične bločne grafe. Nazadnje opišemo konstrukcijo ▫$γ$▫-enoličnih grafov oziroma zapišemo štiri operacije, ki jih lahko uporabimo nad ▫$γ$▫-enoličnimi grafi, da bo na novo dobljen graf ponovno ▫$γ$▫-enoličen.

Keywords

magistrska dela;dominantna množica;γ-enolični grafi;drevesa;bločni grafi;

Data

Language:	Slovenian
Year of publishing:	2023
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[D. Cvetrežnik]
UDC:	519.17(043.2)
COBISS:	181386755
Views:	52
Downloads:	3
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	Graphs with unique γ-sets
Secondary abstract:	The thesis aims to give an in-depth insight into graphs with a unique ▫$γ$▫-sets (known as ▫$γ$▫-unique graphs), that is, graphs with exactly one minimum dominating set. Initially, we present fundamental theoretical concepts and principles of graphs, and examine two distinct classes of graphs, namely trees and block graphs. Subsequently, we provide a detailed description of the dominating set and the domination number of a graph. Then we give some necessary and some sufficient conditions of ▫$γ$▫-unique graphs.▫$γ$▫-unique trees are then studied in more details. We present two characterizations of ▫$γ$▫-unique trees and extend these characterizations to ▫$γ$▫-unique block graphs. In the concluding segment of the thesis, the construction of ▫$γ$▫-unique graphs will be explained by using four graph operations that can be applied on ▫$γ$▫-unique graph, such that the resulting graph is again ▫$γ$▫-unique.
Secondary keywords:	master theses;dominating set;γ-unique graphs;trees;block graphs;Grafične metode;Univerzitetna in visokošolska dela;
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	VIII, 59 f.
ID:	21472852