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Now showing items 1-9 of 9

#### Zero-sum problems in finite cyclic groups

(Brock University, 2009-01-28)

The purpose of this thesis is to investigate some open problems in the area of
combinatorial number theory referred to as zero-sum theory. A zero-sequence in a
finite cyclic group G is said to have the basic property if ...

#### Response curves of deterministic and probabilistic cellular automata in one and two dimensions

(2012-04-02)

One of the most important problems in the theory of cellular automata (CA) is
determining the proportion of cells in a specific state after a given number of time
iterations. We approach this problem using patterns in ...

#### The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

(2012-03-30)

This work consists of a theoretical part and an experimental one. The first part
provides a simple treatment of the celebrated von Neumann minimax theorem as
formulated by Nikaid6 and Sion. It also discusses its relationships ...

#### Rings, Group Rings, and Their Graphs

(Brock University, 2013-09-05)

We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. ...

#### Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles

(Brock University, 2013-09-05)

The conjecture claiming that every planar graph is acyclic 5-choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph ...

#### Edge-choosability of Planar Graphs

(Brock University, 2013-09-26)

According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s ...

#### A game-theoretic network formation model

(Brock University, 2014-07-23)

We study the dynamics of a game-theoretic network formation
model that yields large-scale small-world networks. So far,
mostly stochastic frameworks have been utilized to explain
the emergence of these networks. On the ...

#### Square Root Finding In Graphs

(Brock University, 2013-01-24)

Abstract: Root and root finding are concepts familiar to most
branches of mathematics.
In graph theory, H is a square root of G
and G is the square of H if
two vertices x,y have an edge in G if and only if
x,y are of ...

#### Prime Rational Functions and Integral Polynomials

(Brock University, 2015-01-05)

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. ...