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Browsing by Supervisor "MacGillivray, Gary"

Browsing by Supervisor "MacGillivray, Gary"

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  • Young, Kailyn M. (2011-05-02)
    A 2-dipath k-colouring of an oriented graph G is an assignment of k colours, 1,2, . . . , k, to the vertices of G such that vertices joined by a directed path of length two are assigned different colours. The 2-dipath ...
  • Slobodin, Aaron (2021-07-29)
    Suppose there is a transmitter located at each vertex of a graph G. A k-limited broadcast on G is an assignment of the integers 0,1,...,k to the vertices of G. The integer assigned to the vertex x represents the strength ...
  • Wheeler, Mackenzie J. (2019-08-27)
    Let G = (V,A,E) be a mixed graph and co : V → {1, 2,...,λ} a function such that co is a proper colouring of the underlying graph, Und(G), and co(u) ≠ co(y) when co(v) = co(x), for every pair of arcs (u,v) and (x,y). Such ...
  • Shepherd, Laura Margret Diane (2005)
    A generalization of the circular chromatic number to hypergraphs is devel-oped. Circular colourings of graphs and hypergraphs are first discussed and it is shown that the circular chromatic number of a graph is the same ...
  • Duffy, Christopher (2011-09-02)
    The Firefighter Process models the spread and defence of a fire using a simple graph. We consider the following discrete-time process: at t = 0 some vertex of the graph begins burning. At each subsequent step we may defend ...
  • Swarts, Jacobus Stephanus (2008-12-19)
    In this thesis we examine the computational complexity of certain digraph homomorphism problems. A homomorphism between digraphs, denoted by $f: G \to H$, is a mapping from the vertices of $G$ to the vertices of $H$ such ...
  • Smith, Bethany Joy (2010-01-26)
    Singly-periodic (SP) and doubly-periodic (DP) graphs arc infinite graphs which have translational symmetries in one and two dimensions, respectively. The problem of counting the number of connected components in such graphs ...
  • Halliday, Felicia (2020-01-02)
    This thesis is partitioned into three parts: improving pre-calculus skills of students in an introductory calculus course, the game of Cops and Robber on oriented graphs, and the generalized game of Cops and Robber. In the ...
  • Edwards, Michelle (2010-01-29)
  • Finbow, Stephen (2017-04-13)
    The well studied class of irredundant vertex sets of a graph has been previously shown to be a special case of (a) a “Private Neighbor Cube” of eight classes of vertex subsets and (b) a family of sixty four classes of ...
  • Anderson, Rachel Jean Selma (2014-04-25)
    In discrete mathematics, a convex space is an ordered pair (V,M) where M is a family of subsets of a finite set V , such that: ∅ ∈M, V ∈M, andMis closed under intersection. The elements of M are called convex sets. For a ...
  • Bard, Stefan (2014-12-23)
    Let G be a graph and k be an integer greater than or equal to the chromatic number of G. The k-colouring graph of G is the graph whose vertices are k-colourings of G, with two colourings adjacent if they colour exactly one ...
  • Duffy, Christopher (2015-08-28)
    A mixed graph is a simple graph in which a subset of the edges have been assigned directions to form arcs. For non-negative integers j and k, a (j, k)−mixed graph is a mixed graph with j types of arcs and k types of edges. ...
  • Yang, Feiran (2020-01-03)
    Let G = (V,E) be a graph and f be a function such that f : V -> {0,1,2,..., k}. Let V_f^+ = {v : f(v) > 0}. If for every vertex v not in V_f^+ there exists a vertex w in V_f^+ such that d(v,w) ≤ f(w) then f is called ...
  • Barone, Chedomir Angelo (2008-04-26)
    Let G be a directed graph with a total labeling. The additive arc-weight of an arc xy is the sum of the label on xy and the label on y. The additive directed vertex-weight of a vertex x is the sum of the label on x and ...
  • Johnson, Jesse T. (2020-05-08)
    Circular words, also known as necklaces, are combinatorial objects closely related to linear words. A brief history of circular words is given, from their early conception to present results. We introduce the concept of a ...
  • Yang, Feiran (2015-08-31)
    Let G be a graph and f be a function that maps V to {0,1,2, ..., diam(G)}. Let V+ be the set of all vertices such that f(v) is positive. If for every vertex v not in V+ there exists a vertex w in V+ such that the ...
  • Campbell, Russell J. (2009-12-22)
    We define a variation of injective oriented colouring as reflexive injective oriented colouring, or rio-colouring for short, which requires an oriented colouring to be injective on the neighbourhoods of the underlying ...
  • Dame, Lorraine Frances (2012-08-29)
    The results of this thesis can be used to help identify students at risk of an unsuccessful entry level undergraduate mathematics (ELUM) outcome early in their course by using a student's score on a diagnostic test, using ...