9838630
Domination in Graphs of Minimum Degree Five
Let G=(V,E) be a simple graph. A subset D⊆V is a dominating set of G, if for any vertex x ∈ V−D, there exists a vertex y ∈ D such that xy ∈ E. By using the so-called vertex disjoint paths cover introduced by Reed, in this paper we prove that every graph G on n vertices with minimum degree at least five has a dominating set of order at most 5n/14.
36018188
A note on graphs with largest total k-domination number
1151930
A result on Vizing's conjecture
Let γ(G) denote the domination number of a simple graph G and let G?H denote the Cartesian product of two simple graphs G and H. In this paper we prove that if γ(G)=3, then γ(G?H)?γ(G)γ(H).
35009889
Tree Domination in Graphs
428956
On a generalization of signed total dominating functions of graphs
34040250
Connected domination critical graphs
Abstract A dominating set in a graph G is a connected dominating set of G if it induces a connected subgraph of G . The minimum number of vertices in a connected dominating set of G is called the connected domination number of G , and is denoted by γ c ( G ). The purpose of this paper is to initiate an investigation of those graphs which are critical in the following sense: for each υ, μ ϵ V (G) with υ not adjacent to u , γ c ( G + υ u ) c ( G ). Thus, G is k -γ c -critical if γ c ( G ) = k and for each edge e ∉ E ( G ), γ c ( G + e ) k . First we discuss whether some particular classes of graphs are γ c -critical. Then 2-γ c -critical graphs are characterized. Finally, the properties of the 3-γ c -critical graphs are studied.
16590368
Knowledge Construction in E-Learning - Designing an E-Learning Environment
In the traditional classroom, students learned to depend on tutors for their motivation, direction, goal setting, progress monitoring, self-assessment, and achievement. A fundamental limitation is that students have little opportunity to conduct and manage their learning activities which are important for knowledge construction. e-Learning approaches and applications which are supported by pervasive technologies, have brought in great benefits to the whole society, meanwhile it also has raised many challenging questions. One of the issues that researchers and educators are fully aware is that technologies cannot drive a courseware design for e-Learning. An effective and quality learning requires an employment of appropriate learning theory and paradigms, organisation of contents, as well as methods and techniques of delivery. This paper will introduce our research work in design an e-Learning environment with emphases on instructional design of courseware for e-learning.
15670300
Recognizing dart-free perfect graphs
A graph G is called a Berge graph if neither G nor its complement contains a chordless cycle whose length is odd and at least five; what we call a dart is the graph with vertices u,v,w,x,y and edges uv,vw,uy,vy,wy,xy; a graph is called dart-free if it has no induced subgraph isomorphic to the dart. We present a polynomial-time algorithm to recognize dart-free Berge graphs; this algorithm uses as a subroutine the polynomial-time algorithm for recognizing claw-free Berge graphs designed previously by Chvatal and Sbihi [J. Combin. Theory Ser. B, 44 (1988), pp. 154--176].
34683247
Two classes of perfect graphs
Abstract We present two classes of perfect graphs. The first class is defined through a construction used by Gallai in his investigation of comparability graphs; the second class contains those Berge graphs defined through a forbidden graph on five vertices.
32541131
A method for interactive articulation of information requirements for strategic decision support
Abstract Decision support for strategic management, an extension to the traditional decision support systems, has been seen as an important area of research where the theory, methods and technologies can bring in a great deal of benefit to the whole enterprise at the executive level. The work in the paper first of all examines two paradigms of information provision for strategic decision support. The information requirements for decision-making are studied to reveal that the level of detail, granularity, format of presentation, and broad range of information type are unique for the applications at the strategic level. The provision of relevant information involves articulation of requirements based on the decision problems described by the executive manager. Secondly, this paper presents the MITAIS approach that allows the user to describe a decision problem interactively and assists articulation of the problem into a presentation in a decision space, by prompting possible patterns of decision dimensions. It further assists a configuration of information requirements into an information space, which covers the information required for the identified problem. MITAIS comprises a set of techniques to support articulation of a decision problem into a decision space, configuration of information space and the mapping between these two spaces. A case study has been used throughout the paper to illustrate the method. A critical evaluation of the development of MITAIS has been carried out to assess the validity of the research. Finally, the paper is concluded with suggestions for future work.
45352472
e-Learning Services Provision and Management
With the rapid development of information technology, learners demand effective personalised learning support, which imposes a new learning paradigm in learning content management. Standards as well as best practice in industry and research community have taken place to address the paradigm shift. With respect to this trend, it is recognised that finding learning content which meet personal learning requirements remains challenging. This paper describes a model of e-learning services provision which integrates the best practice in e-learning and Web services technology so that learning content management is capable of supporting applications of learning services.