• Analysis of tree spectra 

      Dadedzi, Kenneth (Stellenbosch : Stellenbosch University, 2018-12)
      ENGLISH ABSTRACT : We study the set of eigenvalues (spectrum) of the adjacency matrix, Laplacian matrix and the distance matrix of trees. In particular, we focus on the distribution of eigenvalues in the spectra of large ...
    • Analytic methods in combinatorial number theory 

      Baker, Liam Bradwin (Stellenbosch : Stellenbosch University, 2015-12)
      ENGLISH ABSTRACT : Two applications of analytic techniques to combinatorial problems with number-theoretic flavours are shown. The first is an application of the real saddle point method to derive second-order asymptotic ...
    • Centrality in random trees 

      Durant, Kevin (Stellenbosch : Stellenbosch University, 2017-12)
      ENGLISH ABSTRACT : We consider two notions of centrality—namely, the betweenness centrality of a node and whether or not it is a centroid—in families of simply generated and increasing trees. Both of these concepts are ...
    • Combinatorics of oriented trees and tree-like structures 

      Okoth, Isaac Owino (Stellenbosch : Stellenbosch University, 2015-03)
      ENGLISH ABSTRACT : In this thesis, a number of combinatorial objects are enumerated. Du and Yin as well as Shin and Zeng (by a different approach) proved an elegant formula for the number of labelled trees with respect ...
    • Contributions to the analysis of approximate counting 

      Prodinger, Helmut (Stellenbosch : Stellenbosch University, 2016-03)
      ENGLISH ABSTRACT : Approximate Counting is a classical technique with very challenging questions re- lated to its performance analysis. It is also somewhat similar to parameters around Digital Search trees. Surprising ...
    • Energy and related graph invariants 

      Andriantiana, Eric Ould Dadah (Stellenbosch : Stellenbosch University, 2013-12)
      Please refer to full text to view abstract.
    • Enumeration of tanglegrams 

      Ravelomanana, Jean Bernoulli (Stellenbosch : Stellenbosch University, 2018-03)
      ENGLISH ABSTRACT : Tanglegrams are graphs obtained by taking two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the two trees. Tanglegrams appear in biology in the study ...
    • Enumeration problems on lattices 

      Ocansey, Evans Doe (Stellenbosch : Stellenbosch University, 2013-03)
      ENGLISH ABSTRACT: The main objective of our study is enumerating spanning trees (G) and perfect matchings PM(G) on graphs G and lattices L. We demonstrate two methods of enumerating spanning trees of any connected ...
    • Limit theorems for integer partitions and their generalisations 

      Ralaivaosaona, Dimbinaina (Stellenbosch : Stellenbosch University, 2012-03)
      ENGLISH ABSTRACT: Various properties of integer partitions are studied in this work, in particular the number of summands, the number of ascents and the multiplicities of parts. We work on random partitions, where all ...
    • The number of independent subsets and the energy of trees 

      Andriantiana, Eric Ould Dadah (Stellenbosch : University of Stellenbosch, 2010-12)
      ENGLISH ABSTRACT: See full text for abstract
    • On a generalisation of k-Dyck paths 

      Selkirk, Sarah Jane (Stellenbosch : Stellenbosch University, 2019-12)
      ENGLISH ABSTRACT: (Refer to full text abstract for symbols that did not transfer correctly). We consider a family of non-negative lattice paths consisting of the step set f(1; 1); (1;􀀀k)g called k-Dyck paths, which are ...
    • On the inducibility of rooted trees 

      Dossou-Olory, Audace Amen Vioutou (Stellenbosch : Stellenbosch University, 2018-12)
      ENGLISH ABSTRACT : The density of appearances of a fixed tree in a larger tree is examined for rooted trees without vertices of outdegree 1 (also known as topological trees). Given a topological tree S with k leaves and ...
    • Properties of graph polynomials and related parameters 

      Misanantenaina, Valisoa Razanajatovo (Stellenbosch : Stellenbosch University, 2017-12)
      ENGLISH ABSTRACT : In this thesis, we investigate various problems related to graph polynomials. We first define two-variable polynomials for rooted trees and specific posets, which are motivated by the Tutte polynomial. ...
    • Properties of greedy trees 

      Razanajatovo Misanantenaina, Valisoa (Stellenbosch : Stellenbosch University, 2014-12)
      ENGLISH ABSTRACT: A greedy tree is constructed from a given degree sequence using a simple greedy algorithm that assigns the highest degree to the root, the second, the third, . . . , -highest degree to the root’s ...
    • Random walk hitting times in random trees 

      Oosthuizen, Joubert (Stellenbosch : Stellenbosch University, 2017-12)
      ENGLISH ABSTRACT : The hitting time Hxy, between two vertices x and y of a graph, is the average time that the standard simple random walk takes to get from x to y. We start by giving a recursive formula for higher moments ...
    • Random walks on graphs 

      Oosthuizen, Joubert (Stellenbosch : Stellenbosch University, 2014-04)
      ENGLISH ABSTRACT: We study random walks on nite graphs. The reader is introduced to general Markov chains before we move on more specifically to random walks on graphs. A random walk on a graph is just a Markov chain ...
    • Spectral radii of matrices associated with graphs 

      Dadedzi, Kenneth (Stellenbosch : Stellenbosch University, 2015-12)
      ENGLISH ABSTRACT : The spectral radius of a graph is defined as the largest absolute value of the eigenvalues of a matrix associated with the graph. In this thesis, we study the spectral radii of the adjacency matrix, ...
    • Torsion bounds for Drinfeld modules with complex multiplication 

      Rabenantoandro, Andry Nirina (Stellenbosch : Stellenbosch University., 2020-04)
      ENGLISH ABSTRACT: The main objective of the present thesis is to prove an analogue for Drinfeld modules of a theorem due to Clark and Pollack. The cardinality of the group of K-rational torsion points of an elliptic curve ...