Now showing items 1-12 of 12

• #### A Brief Exploration of Total Colouring ﻿

(2017-09-05)
A total colouring of a graph is an assignment of colours to the edges and vertices such that adjacent objects receive different colours. In this thesis, we prove partial results towards the Total Colouring Conjecture which ...
• #### Burning a Graph as a Model for the Spread of Social Contagion ﻿

(2016-04-08)
The spread of social contagion is an active area in social network analysis. Assume that we want to spread a message among all the users of a network. Knowing the structure of the network, we may ask how fast can we do ...
• #### DOMINATION POLYNOMIALS: A BRIEF SURVEY AND ANALYSIS ﻿

(2017-08-18)
A dominating set S of a graph G of order n is a subset of the vertices of G such that every vertex is either in S or adjacent to a vertex of S. The domination polynomial of G, denoted D(G, x), is the generating polynomial ...
• #### EXISTENTIALLY CLOSED PROPERTY IN DIRECTED INFINITE GRAPHS ﻿

(2018-07-18)
Graph theory abounds with applications inside mathematics itself, and in computer science, and engineering. One direction of research within graph theory is the topic of inﬁnite graphs, which is the focus of this thesis. ...
• #### Majority Voter Model for Information Diffusion ﻿

(2019-08-29)
A Majority Voter Model is a iterative process on graphs. Let G be a graph with a initial vertex colouring of n colours with the option of a vertex being uncoloured. The is a sequential process where once a vertex is coloured, ...
• #### On Dominating Sets and the Domination Polynomial ﻿

(2021-08-31)
A dominating set S of a graph G of order n is a subset of the vertices of G such that every vertex is either in S or adjacent to a vertex of S. The domination polynomial is denoted by D(G,x) is the generating polynomial ...
• #### On the Neighbourhood Polynomial ﻿

(2017-04-07)
The neighbourhood polynomial of a graph is the generating function for the neighbourhood complex, which contains all subsets of vertices which have a common neighbour. We begin with some formulas for computing the neighbourhood ...
• #### On Variants of Diffusion ﻿

(2020-04-13)
This thesis will examine the Chip Firing variant, diffusion, in many of its different iterations. We will look at a previously studied version, Parallel Diffusion, along with four new variants: Quantum Parallel Diffusion, ...
• #### SAFE GAME OF COMPETITIVE DIFFUSION ﻿

(2014-04-03)
Competitive Diffusion is a recently introduced game-theoretic model for the spread of information through social networks. The model is a game on a graph with external players trying to reach the most vertices. In this ...
• #### Split Reliability ﻿

(2021-08-06)
The split reliability of a graph G is the probability that if every edge is independently operational with probability p, every vertex is always operational, and we specify two vertices s and t, that every vertex can ...
• #### Well-Distributed Sets on Graphs ﻿

(2018-08-15)
Location theory is a topic widely researched in mathematics and computer science. The goal of this thesis will be to propose a new method for choosing vertices on a graph “optimally”, in terms of spread, by generalizing ...
• #### Zero-Forcing Processes on Proper Interval Graphs and Twisted Hypercubes ﻿

(2023-04-22)
Zero forcing is a graph infection process where a colour change rule is applied iteratively to a graph and an initial set of vertices, S. If S results in the entire graph becoming infected, we call this set a zero forcing ...