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Title:Robne množice v grafih
Authors:Mernik, Lucija (Author)
tepeh, aleksandra (Mentor) More about this mentor... New window
Files:.pdf UNI_Mernik_Lucija_2013.pdf (1,34 MB)
 
Language:Slovenian
Work type:Undergraduate thesis (m5)
Typology:2.11 - Undergraduate Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:V diplomskem delu raziskujemo različne tipe robnih vozlišč: periferna, konturna in ekscentrična vozlišča. Predstavimo osnovne koncepte teorije grafov s poudarkom na standardnih produktih grafov, se osredotočimo na različne tipe robnih množic in predstavimo številne njihove strukturne lastnosti. Iz glavnega izreka je razviden obstoj grafa s predpisano močjo periferne, konturne, ekscentrične in robne množice. Pokažemo tudi, da je robna množica vsakega povezanega grafa tudi geodetska in predstavimo nekaj zadostnih pogojev za to, da je konturna množica grafa tudi geodetska. Na koncu naredimo pregled znanih rezultatov glede robnih množic v standardnih produktih grafov.
Keywords:robne množice, produkti grafov, konturna množica.
Year of publishing:2013
Publisher:[L. Mernik]
Source:Maribor
UDC:51(043.2)
COBISS_ID:19877896 Link is opened in a new window
NUK URN:URN:SI:UM:DK:VEMJIJIX
Views:1173
Downloads:88
Metadata:XML RDF-CHPDL DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:Boundary sets in graphs
Abstract:Graduation thesis investigates different types of boundary vertices: peripheral, contour and eccentric vertices. The basic concepts of graph theory are presented with the emphasis on the standard products of graphs and focus our attention on several types of boundary vertices, obtaining a number of basic structural properties. The main theorem shows the existence of a graph with the prescribed cardinality of the periphery, contour, eccentric and boundary sets, respectively. We also show that the boundary of every connected graph is a geodetic set, and present several sufficient conditions for the contour set to be a geodetic set. In the end we summarize known results about boundary type sets in standard products of graphs.
Keywords:boundary sets, products of graphs, contour set.


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