Distances between graphs under edge operations

AbstractWe investigate three metrics on the isomorphism classes of graphs derived from elementary edge operations: the edge move, rotation and slide distances. We derive relations between the metrics, and bounds on the distance between arbitrary graphs and between arbitrary trees. We also consider the sensitivity of the metrics to various graph operations

Maximum and minimum toughness of graphs of small genus

AbstractA new lower bound on the toughness t(G) of a graph G in terms of its connectivity ϰ(G) and genus γ(G) is obtained. For γ > 0, the bound is sharp via an infinite class of extremal graphs all of girth 4. For planar graphs, the bound is t(G) > ϰ(G)/2 − 1. For ϰ = 1 this bound is not sharp, but for each ϰ = 3, 4, 5 and any ϵ > 0, infinite families of graphs {G(ϰ, ϵ)} are provided with ϰ(G(ϰ, ϵ)) = ϰ, but t(G(ϰ, ϵ)) < ϰ/2 − 1 + ϵ.Analogous investigations on the torus are carried out, and finally the question of upper bounds is discussed. Several unanswered questions are posed

An algebraic approach to sesqui-linear curves in Desarguesian planes

Thesis (D. Sc.) -- University of Stellenbosch, 1970.Full text to be digitised and attached to bibliographic record