A benzenoid is a molecule that can be represented as a graph. This graph is a fragment of the hexagon lattice. A dominating set $D$ in a graph $G$ is a set of vertices such that each vertex of the graph is either in $D$ or adjacent to a vertex in $D$. The domination number $\gamma=\gamma(G)$ of a graph $G$ is the size of a minimum dominating set. We will find formulas and bounds for the domination number of various special benzenoids, namely, linear chains $L(h)$, triangulenes $T_k$, and parallelogram benzenoids $B_{p,q}$. The domination ratio of a graph $G$ is $\frac{\gamma(G)}{n(G)}$, where $n(G)$ is the number of vertices of $G$. We will use the preceding results to prove that the domination ratio is no more than $\frac{1}{3}$ for the considered benzenoids. We conjecture that is true for all benzenoids.

Thesis (Ph. D.)--University of California, 1911. / Cover title. "Sonderabdruck aus dem Archiv für entwicklungsmechanik der organismen ... XXXIV. Band, 1. Heft."

Thesis (M.S.)--Virginia Commonwealth University, 2010. / Prepared for: Dept. of Mathematics and Applied Mathematics. Title from title-page of electronic thesis. Bibliography: leaf 35.

Thesis (Ph. D.)--University of California, 1911. / Cover title. "Sonderabdruck aus dem Archiv für entwicklungsmechanik der organismen ... XXXIV. Band, 1. Heft."

1. The Nature of the Problem: Cerebral dominance and its relationship to the problems of handedness and disorders of the language function are discussed n detail, with comparisons of the theories put for - and by different authorities. 2. How it can be tackled: The essential requirement is early diagnosis and treatment of the syndrome, and emphasis is given throughout to the importance of early ascertainment. Long- standing cases require lengthy individual treatment, and therefore those in contact with the pre-school child must have training o enable them to recognise early signs, and to give advice at the outset. 3. Results to be expected; It is stressed throughout that the prognosis is good, provided that treatment is undertaken early. If cases with the specific reading disability are ascertained at the very beginning, the results of treatment are uniiformly good, and as a rule, no permanent disability remains.

Vizing conjectured in 1963 that the domination number of the Cartesian product of two graphs is at least the product of their domination numbers; this remains one of the biggest open problems in the study of domination in graphs. Several partial results have been proven, but the conjecture has yet to be proven in general. The purpose of this thesis was to study Vizing's conjecture, related results, and open problems related to the conjecture. We give a survey of classes of graphs that are known to satisfy the conjecture, and of Vizing-like inequalities and conjectures for different types of domination and graph products. We also give an improvement of the Clark-Suen inequality. Some partial results about fair domination are presented, and we summarize some open problems related to Vizing's conjecture.

A graph G is domination bicritical if the removal of any pair of vertices decreases the domination number. Properties of bicritical graphs are studied. We show that a connected bicritical graph has domination number at least 3, minimum degree at least 3, and edge-connectivity at least 2. Ways of constructing a bicritical graph from smaller bicritical graphs are presented.

Given a digraph D = (V, A), with vertex set V and arc set A, a set S ⊆ V is a dominating set if for every vertex v in V \ S, there are a vertex u in S and an arc (u, v) from u to v. In this chapter we consider the counterparts in directed graphs of independent, dominating, independent dominating, and total dominating sets in undirected graphs.

In this chapter, we discuss dominating functions in graphs, a concept birthed by Stephen Hedetniemi in the mid 1980s.

The aim of my dissertation is to contribute to the development of the Czech Republic language policy. The EU policy aims to promote cross-border cohesion, which causes identity and language shift. It is necessary to monitor these processes and revise them. That's why I submit my study dealing with a bilingual education project in Czech-German borderland. In the chapter I. Language and Identity I describe ethnic identity experience, language a/symmetry (in language competencies and use of Czech and German languages) and asymmetry influence on both nations relation. In the chapter II. Dominance and Power I characterize relations between Czech and German children, their submisivity or dominancy. So I observe the dynamics of dialogue; interactional dominance and interactional modality / speech style. I subordinate the methodology to the research aim. In both chapters the social reality observable in common conversation is described. That's why I choose cross-disciplinary approaches; ethnography of communication, ethnomethodology, discourse analysis and dialogue analysis. I use records of authentic conversations between teachers and children I taped during their common walks and on mixed rooms. I analyzed 440 minutes of interethnic communication. Subsequently I examined 1.763 turns in detail (by qualitative and...