Izračun števila prirejanj v katakondenziranih benzenoidnih sistemih : delo diplomskega seminarja

Grad, Simon (author), Klavžar, Sandi (mentor)

V diplomskem delu obravnavamo tematiko s področja kemijske teorije grafov. Hosoyev indeks (Z indeks) grafa $G$ je definiran kot $Z(G) = \sum_{k \geq 0} p(G,k)$, kjer $p(G,k)$ označuje število $k$-prirejanj v grafu $G$ in je povezan z mnogimi termodinamičnimi lastnostmi kot so vrelišče, entropija in skupna $\pi$-elektronska energija. Cilj diplomskega dela je s pomočjo matrik predstaviti način, kako lahko izračunamo Hosoyev indeks v poljubnem katakondenziranem benzenoidnem sistemu.

• Language: Slovenian
• Keywords: kemijska teorija grafov, prirejanje, število k-prirejanj, Hosoyev indeks, katakondenziran benzenoidni sistem
• Work type: Bachelor thesis/paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-150828
• UDC: 519.17
• COBISS.SI-ID: 165622019
• Publication date in RUL: 24.09.2023

Secondary language

• Language: English
• Title: Computing the Number of Matchings in Catacondensed Benzenoid Systems

Abstract

The thesis deals with topics from the field of chemical graph theory. The Hosoya index of a graph $G$ is defined as ${Z(G) = \sum_{k \geq 0} p(G,k)}$, where $p(G,k)$ is the number of $k$-matchings in the graph $G$, and is associated with many thermodynamic properties such as boiling point, entropy and total $\pi$-electron energy. The aim of this thesis is to present a way to compute the Hosoya index of catacondensed benzenoid systems with transfer matrix technique.

• Keywords: chemical graph theory, matching, number of k-matchings, Hosoya index, catacondensed benzenoid system