• Analysis of tree spectra 

      Dadedzi, Kenneth (2018-12-01)
    • 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 (2018-10-12)
    • 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, ...