<p>In the course of exploring various symmetries of vertex-transitive graphs, we introduce the concept of quasi-normal subgroups in groups. This is done since the symmetries of vertex-transitive graphs are intimately linked to those, fait accompli, of groups. With this, we ask if the concept of strongly simple groups has a place for consideration. We have shown that for n &gt / 5, An, the alternating group on n odd elements, is not strongly simple.</p>

3D graphics pipeline can be divided into two subsystems: geometry subsystem and rendering subsystem. Hardware implementation of the transformation and lighting in the geometric subsystem can be divided into two categories, fixed function pipeline and programmable vertex shader. This thesis proposes a programmable vertex shader design based on OpenGL ES 2.0 specification. We start from the design of instruction set and use a multiplier-accumulator (MAC)-based SIMD (Single-Instruction Multiple-Data) structure. The vertex shader supports both floating-point and fixed-point operations of both scalar and vector formats. In addition, the special function unit for calculation of complicated functions is also integrated in the vertex shader. Besides, we also make out best to minimize the cost, power ,and delay during the entire design process.

<p>In the course of exploring various symmetries of vertex-transitive graphs, we introduce the concept of quasi-normal subgroups in groups. This is done since the symmetries of vertex-transitive graphs are intimately linked to those, fait accompli, of groups. With this, we ask if the concept of strongly simple groups has a place for consideration. We have shown that for n &gt / 5, An, the alternating group on n odd elements, is not strongly simple.</p>

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1995. / Includes bibliographical references (p. 80-85).

Magister Scientiae - MSc / In the course of exploring various symmetries of vertex-transitive graphs, we introduce the concept of quasi-normal subgroups in groups. This is done since the symmetries of vertex-transitive graphs are intimately linked to those, fait accompli, of groups. With this, we ask if the concept of strongly simple groups has a place for consideration. / South Africa

Let G=(V,E) be a graph with vertex set V and edge set E. A vertex v∈V ve-dominates every edge incident to it as well as every edge adjacent to these incident edges. The vertex–edge degree of a vertex v is the number of edges ve-dominated by v. Similarly, an edge e=uv ev-dominates the two vertices u and v incident to it, as well as every vertex adjacent to u or v. The edge–vertex degree of an edge e is the number of vertices ev-dominated by edge e. In this paper we introduce these types of degrees and study their properties.

In this thesis we present the connection between vertex operator algebras and modular forms which lies at the heart of Borcherds’ proof of the Monstrous Moonshine conjecture. In order to do so we introduce modular forms, vertex algebras, vertex operator algebras and their partition functions. Each notion is illustrated with examples.

A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination vertex removal stable if the removal of an arbitrary vertex leaves the total domination number unchanged. On the other hand, a graph is total domination vertex removal changing if the removal of an arbitrary vertex changes the total domination number. In this paper, we study total domination vertex removal changing and stable graphs.

For a vertex x of G, the eccentricity e (x) is the distance between x and a vertex farthest from x. Then x is a contour vertex if there is no neighbor of x with its eccentricity greater than e (x). The x-y path of length d (x,y) is called a x-y geodesic. The geodetic interval I [x,y] of a graph G is the set of vertices of all x-y geodesics in G. For S ⊆ V , the geodetic closure I [S] of S is the union of all geodetic intervals I [x,y] over all pairs x,y ∈S. A vertex set S is a geodetic set for G if I [S] = V (G). In this thesis, we study the contour sets of product graphs and discuss these sets are geodetic sets for some conditions.

Universiẗat, Diss.--Paderborn, 1985.