Molekularne invariante, porojene iz ekscentričnosti vozlišč

delo diplomskega seminarja

Matija Kerkoč (Author), Sandi Klavžar (Mentor)

Abstract

Molekularne invariante (včasih imenovane tudi topološki indeksi) so lastnosti grafov, ki jih uporabljamo za napovedovanje kemijskih ter bioloških lastnosti molekul na podlagi strukturnih lastnosti njim prirejenih grafov. Nekatere med njimi so se izkazale za učinkovito sredstvo v matematični kemiji. V delu bomo predstavili nekaj najbolj znanih invariant, podrobneje pa bomo predstavili indeks ekscentričnost-stopnja, ki je ena izmed novejših invariant, ki so se izkazale za najbolj učinkovite. Podali bomo eksplicitne formule za izračun indeksa ekscentričnost-stopnja za benzenoidne grafe. Vpeljali bomo pojem kartezičnega produkta grafov, ki je naravna struktura mnogih družin kemijskih molekul. Naš končni cilj pa bo izpeljava eksplicitne formule za izračun indeksa ekscentričnost-stopnja v kartezičnem produktu.

Keywords

matematika;ekscentričnost grafa;benzenoidni grafi;grafovske invariante;kartezični produkt grafov;indeks ekscentričnost-stopnja;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[M. Kerkoč]
UDC:	519.1
COBISS:	18724953
Views:	1925
Downloads:	209
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Eccentricity based molecular invariants
Secondary abstract:	Molecular invariants (also known as topological indices) has proven themselves as good predictors of chemical and biological activities. We can apply exact formulas on hydrogen stripped chemical graphs and try to predict chemical activity of molecules based on their structure. In this diploma thesis we will define several molecular invariants with emphasis on eccentric connectivity index which is one of novel molecular invariants. We will compute exact formulas for different families of benzenoid graphs. We will then define Cartesian product of graphs, which is a natural structure in several chemical molecules. Our final goal is to obtain an explicit formula for eccentric connectivity index in Cartesian products.
Secondary keywords:	mathematics;graph eccentricity;benzenoid graphs;graph invariants;Cartesian graph product;eccentric connectivity index;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	26 str.
ID:	11223570