Robne in geodetske množice v grafih

Lebar, Vesna

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Title:	Robne in geodetske množice v grafih
Authors:	ID Lebar, Vesna (Author) ID Brešar, Boštjan (Mentor) More about this mentor...
Files:	MAG_Lebar_Vesna_2015.pdf (1,41 MB) MD5: 6AA539DE23FDC1813E552331C4345C5B
Language:	Slovenian
Work type:	Master's thesis/paper
Typology:	2.09 - Master's Thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	V magistrskem delu so obravnavane lastnosti in povezave med posameznimi robnimi množicami grafa, ki jih sestavljajo robna, ekscentrična, periferna, konturna in ekstremna vozlišča grafa. Zanimale nas bodo predvsem povezave med robnimi in geodetskimi množicami grafa, posebej se bomo posvetili preučevanju konturne množice grafa. V prvem poglavju so zapisani osnovni pojmi in definicije iz teorije grafov, ki jih bomo potrebovali v nadaljevanju. V drugem poglavju definiramo tipe robnih množic, navedemo osnovne lastnosti le-teh in dokažemo dva realizacijska izreka, ki govorita o obstoju poljubnega grafa pri podanih kardinalnostih različnih skupin robnih množic. V tretjem poglavju navedemo rezultate, ki pravijo, da je konturna množica tetivnih, razdaljno hereditarnih, 3-SDH in HHD-prostih grafov geodetska množica. Obravnavamo tudi konturno množico dvodelnih grafov in dokažemo, da za vsak diameter $kgeq 8$ obstaja dvodelni graf, katerega konturna množica ni geodetska. V zadnjem razdelku obravnavamo konturne in geodetske množice delnih kock.
Keywords:	robne množice, geodetska množica, konturna množica
Place of publishing:	Maribor
Publisher:	[V. Lebar]
Year of publishing:	2015
PID:	20.500.12556/DKUM-54644
UDC:	519.17(043.2)
COBISS.SI-ID:	21693192
NUK URN:	URN:SI:UM:DK:ODME7TH4
Publication date in DKUM:	05.11.2015
Views:	1576
Downloads:	134
Metadata:
Categories:	FNM
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Secondary language

Language:	English
Title:	Boundary and geodetic sets in graphs
Abstract:	In this master thesis we are dealing with the properties and relationships between boundary sets of a graph consisting of boundary, eccentric, peripheral, contour and extreme vertices of a graph. We study mostly the relationship between boundary sets and geodetic sets of an arbitrary graph, in particular we focus on the contour set of a graph. The first chapter introduces some basic definitions from graph theory that are needed for further understanding of the subject. In the second chapter we define different types of boundary sets and obtain some basic structural properties. We prove two realization theorems, which are referring to the existence of a graph, where cardinalities of different groups of boundary sets are given. In the third section we present results stating that the contour set of chordal, distance hereditary, 3-SDH and HHD-free graphs is the geodetic set. We also focus on the contour set of bipartite graphs and prove that for every diameter $kgeq 8$ there exists a bipartite graph, whose contour set is not a geodetic set. In the last section we study contour and geodetic sets of partial cubes.
Keywords:	boundary sets, geodetic set, contour set

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