Važnost i zalihost bridova u grafovima

master's thesis

• Author: Ana Vidaček
• Mentor: Tomislav Došlić (mentor)
• Committee member: Tomislav Došlić (predsjednik povjerenstva)
• Committee member: Vedran Krčadinac (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Dragutin Svrtan (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-11-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu smo izračunali važnost i zalihost bridova u nekim klasama grafova. Na početku smo naveli osnovne pojmove vezane uz teoriju grafova te definirali savršeno sparivanje u grafu, važnost i zalihost bridova. Nakon toga smo uzeli sedam klasa grafova pa odredili broj savršenih sparivanja i važnost i zalihost bridova u tim grafovima. Grafovi koje smo promatrali su \(Z_n\) koji se sastoji od \(n\) šesterokuta pozicioniranih u cik-cak poziciji, \(L_n\) koji se sastoji od \(n\) četverokuta pozicioniranih jedan do drugog, \( \Pi_n\) koji je uspravna piramida, \(R_n\) koji je uspravna prizma, \(A_n\) koji se sastoji od \(n\) pravilnih šesterokuta pozicioniranih jedan do drugog, \(B_n\) koji je bipiramida i \(Q_n\) koji je \(n\)-dimenzionalna hiperkocka. Na kraju smo naveli primjenu pojma važnosti i zalihosti u kemiji, točnije u računanju sadržaja \(\pi\)-elektrona prstenova u benzenoidnim paralelogramima.

Abstract (english)

In this graduate thesis we calculated the importance and redundancy of edges in some classes of graphs. At the beginning we mentioned the basic concepts related to graph theory and define the perfect matching in a graph, and the importance and redundancy. After that we took seven classes of graphs and determine the number of perfect matchings and importance and redundancy in these graphs. Graphs that we observed are \(Z_n\) which consists of \(n\) hexagons positioned in zigzag position, \(L_n\) which consists of \(n\) quadrilaterals positioned next to each other, \( \Pi_n\) which is a pyramid, \(R_n\) which is a prism graph, \(A_n\) which consists of \(n\) hexagons positioned next to each other, \(B_n\) which is a bipyramid, and \(Q_n\) which is a hypercube graph. At the end of this thesis we make use of terms importance and redundancy in chemistry, more specifically for \(\pi\)-electron content of rings in benzenoid parallelograms.

• Keywords: teorija grafova; savršena sparivanja; važnost i zalihost bridova
• Keywords (english): graph theory; perfect matching; importance and redundancy of edges
• Language: croatian
• URN:NBN: urn:nbn:hr:217:118293
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-03-30 12:10:14