• 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 ...
    • 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 ...
    • 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 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 ...
    • 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, ...