For a connected graph $ G $ of order at least $2 $ and $ S\subseteq V (G) $, the\emph
{Steiner distance} $ d_G (S) $ among the vertices of $ S $ is the minimum size among all …

In this paper we present bounds on the radius and diameter of graphs of girth at least 6 and
for (C 4, C 5)-free graphs, ie, graphs not containing cycles of length 4 or 5. We show that the …

Let G be a connected graph of order p and S a nonempty set of vertices of G. Then the
Steiner distance d (S) of S is the minimum size of a connected subgraph of G whose vertex …

A graph is n-existentially closed if, for all disjoint sets of vertices A and B with| A∪ B|= n,
there is a vertex z not in A∪ B adjacent to each vertex of A and to no vertex of B. In this …

In this thesis, we present results from multiple projects with the theme of extending results
from graphs to hypergraphs. We first discuss the existential closure property in graphs, a …

The study described in this thesis was carried out in the School of Mathematical Sciences,
University of KwaZulu-Natal, Durban, during the period May 2008 to December 2011. This …

Many studies on complex networks focus on how to characterize them and what are the
most relevant measures for understanding their structure. In particular, the degree …

The research work presented in this thesis consists of investigation of bounds on the four
most important distance measures (radius, diameter/fault-diameter, average eccentricity and …