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Irregularity Strength of Graphs
Marcin Anholcer
Abstract
One of the well-known facts about simple graphs is that in every such graph G there are at least two vertices of the same degree (it follows from the Pigeonhole Principle).The situation changes when we assign weights (being positive integers) either to the edges of G or to its edges and vertices and consider weighted degrees of vertices instead of the ordinary ones. Three graph parameters are considered in the thesis: irregularity strength s(G), total vertex irregularity strength tvs(G) and product irregularity strength ps(G). In the first chapter of the thesis upper bounds on tvs(G) of arbitrary graph G ar given. The author presents also the exact values of tvs(F), where F is a forest with no vertices of degree 2, and tvs(Cnk), where Cnk is the k-th power of cycle Cn.The second chapter contains the results on the irregularity strength, s(G). In particular, the exact value of s(Cnk) has been determined.In the last chapter the facts on the product irregularity strength are presented. The main results are the upper bounds on ps(G) for G being either cycle or grid of sufficiently many vertices.- Record ID
- UAM7e75dd23565c4b4585d3ac20d30e06c9
- Diploma type
- Doctor of Philosophy
- Author
- Title in Polish
- Siła nieregularności grafów
- Title in English
- Irregularity Strength of Graphs
- Language
- pol (pl) Polish
- Certifying Unit
- Faculty of Mathematics and Computer Science (SNŚ/WMiI/FoMaCS)
- Discipline
- mathematics / (mathematics domain) / (physical sciences)
- Scientific discipline (2.0)
- Status
- Finished
- Defense Date
- 28-12-2010
- Title date
- 28-12-2010
- Supervisor
- URL
- http://hdl.handle.net/10593/782 Opening in a new tab
- Keywords in English
- Irregularity strength, Total vertex, Irregularity strength, Product irregularity strength, Irregular weighting
- Abstract in English
- One of the well-known facts about simple graphs is that in every such graph G there are at least two vertices of the same degree (it follows from the Pigeonhole Principle).The situation changes when we assign weights (being positive integers) either to the edges of G or to its edges and vertices and consider weighted degrees of vertices instead of the ordinary ones. Three graph parameters are considered in the thesis: irregularity strength s(G), total vertex irregularity strength tvs(G) and product irregularity strength ps(G). In the first chapter of the thesis upper bounds on tvs(G) of arbitrary graph G ar given. The author presents also the exact values of tvs(F), where F is a forest with no vertices of degree 2, and tvs(Cnk), where Cnk is the k-th power of cycle Cn.The second chapter contains the results on the irregularity strength, s(G). In particular, the exact value of s(Cnk) has been determined.In the last chapter the facts on the product irregularity strength are presented. The main results are the upper bounds on ps(G) for G being either cycle or grid of sufficiently many vertices.
- Thesis file
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- File: 1
- Siła nieregularności grafów, File Anholcer_Marcin_doktorat.pdf / 753 KB
- Anholcer_Marcin_doktorat.pdf
- publication date: 02-01-2020
- Siła nieregularności grafów, File Anholcer_Marcin_doktorat.pdf / 753 KB
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- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/phd/UAM7e75dd23565c4b4585d3ac20d30e06c9/
- URN
urn:amu-prod:UAM7e75dd23565c4b4585d3ac20d30e06c9