Super edge-magic deficiency of join-product graphs

A graph $G$ is called \textit{super edge-magic} if there exists a bijective function $f$ from $V(G) \cup E(G)$ to $\{1, 2, \ldots, |V(G) \cup E(G)|\}$ such that $f(V(G)) = \{1, 2, \ldots, |V(G)|\}$ and $f(x) + f(xy) + f(y)$ is a constant $k$ for every edge $xy$ of $G$. Furthermore, the \textit{super edge-magic deficiency} of a graph $G$ is either the minimum nonnegative integer $n$ such that $G \cup nK_1$ is super edge-magic or $+\infty$ if there exists no such integer. \emph{Join product} of two graphs is their graph union with additional edges that connect all vertices of the first graph to each vertex of the second graph. In this paper, we study the super edge-magic deficiencies of a wheel minus an edge and join products of a path, a star, and a cycle, respectively, with isolated vertices.Comment: 11 page

Magic and antimagic labeling of graphs

"A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling."Doctor of Philosoph

Four Lessons in Versatility or How Query Languages Adapt to the Web

Exposing not only human-centered information, but machine-processable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the Web into islands of data, each in different Web formats: Some providers choose XML, others RDF, again others JSON or OWL, for their data, even in similar domains. This fracturing stifles innovation as application builders have to cope not only with one Web stack (e.g., XML technology) but with several ones, each of considerable complexity. With Xcerpt we have developed a rule- and pattern based query language that aims to give shield application builders from much of this complexity: In a single query language XML and RDF data can be accessed, processed, combined, and re-published. Though the need for combined access to XML and RDF data has been recognized in previous work (including the W3C’s GRDDL), our approach differs in four main aspects: (1) We provide a single language (rather than two separate or embedded languages), thus minimizing the conceptual overhead of dealing with disparate data formats. (2) Both the declarative (logic-based) and the operational semantics are unified in that they apply for querying XML and RDF in the same way. (3) We show that the resulting query language can be implemented reusing traditional database technology, if desirable. Nevertheless, we also give a unified evaluation approach based on interval labelings of graphs that is at least as fast as existing approaches for tree-shaped XML data, yet provides linear time and space querying also for many RDF graphs. We believe that Web query languages are the right tool for declarative data access in Web applications and that Xcerpt is a significant step towards a more convenient, yet highly efficient data access in a “Web of Data”

Contributions to the cornerstones of interaction in visualization: strengthening the interaction of visualization

Visualization has become an accepted means for data exploration and analysis. Although interaction is an important component of visualization approaches, current visualization research pays less attention to interaction than to aspects of the graphical representation. Therefore, the goal of this work is to strengthen the interaction side of visualization. To this end, we establish a unified view on interaction in visualization. This unified view covers four cornerstones: the data, the tasks, the technology, and the human.Visualisierung hat sich zu einem unverzichtbaren Werkzeug für die Exploration und Analyse von Daten entwickelt. Obwohl Interaktion ein wichtiger Bestandteil solcher Werkzeuge ist, wird der Interaktion in der aktuellen Visualisierungsforschung weniger Aufmerksamkeit gewidmet als Aspekten der graphischen Repräsentation. Daher ist es das Ziel dieser Arbeit, die Interaktion im Bereich der Visualisierung zu stärken. Hierzu wird eine einheitliche Sicht auf Interaktion in der Visualisierung entwickelt

Language Learning Activity Paradigm

In this study, I investigate the application of active learning approaches, with the help of call and mall frameworks. These interactive learning solutions emphasize learner-created content, with the goal of improving the vocabulary development of grade 7 students. It is assumed that the use of computer and mobile technologies can increase the capacity for learning vocabulary. With a concept prototype, that demonstrates the translation of a textually based Language Arts lesson plan into a visual paradigm for active learning, I create a more porous and malleable language learning model for the Google Generation. My hypothesis is that this prototype will benefit the learning of Language Arts for 7th grade students. Such an instrument could ultimately provide students with the opportunity to engage in knowledge creation and sharing across formal and informal learning environments. The methodology used for this thesis essay begins with defining a problem by utilising both academic and qualitative studies. This is followed by the collecting of evidence from alternative learning approaches, which are defined by their various strengths and deficiencies through product analysis, case studies and theoretical grounds. The essay concludes with a proposed design and concept prototype testing, which I have called The Language Learning Activity Paradigm (llap)