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Title: Robne množice v grafih Mernik, Lucija (Author)tepeh, aleksandra (Mentor) More about this mentor... UNI_Mernik_Lucija_2013.pdf (1,34 MB) Slovenian Undergraduate thesis (m5) 2.11 - Undergraduate Thesis FNM - Faculty of Natural Sciences and Mathematics 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. robne množice, produkti grafov, konturna množica. 2013 [L. Mernik] Maribor 51(043.2) 19877896 URN:SI:UM:DK:VEMJIJIX 1173 88 FNM

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## Secondary language

Language: English Boundary sets in graphs 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. boundary sets, products of graphs, contour set.