206571042
An Upper Bound for the Independent Domination Number
Let G be a simple graph of order n and minimum degree ?. The independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. In this paper, we show that i(G)?n+2??2n?. Thus a conjecture of Favaron is settled in the affirmative.
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.
29305561
Positively curved cubic plane graphs are finite
Let G be an infinite plane graph such that G is locally finite and every face of G is bounded by a cycle. Then G is said to be positively curved if, for every vertex x of G, 1− d(x)/2 + Σx∈F 1 |F | > 0, where the summation is taken over all facial cycles F containing x. Note that if G is positively curved then the maximum degree of G is at most 5. As a discrete analogue of a result in Riemannian geometry, Higuchi conjectured that if G is positively curved then G is finite. In this paper, we establish this conjecture for cubic graphs. Partially supported by a grant from China Scholarship Council Partially supported by NSF grant DMS-9970527
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).
21127516
On independent domination number of regular graphs
Abstract Let G be a simple graph. The independent domination number i ( G ) is the minimum cardinality among all maximal independent sets of G . Haviland (1995) conjectured that any connected regular graph G of order n and degree δ ⩽ n /2 satisfies i ( G ) ⩽ ⌈2 n /3 δ ⌉ δ /2. In this paper, we will settle the conjecture of Haviland in the negative by constructing counterexamples. Therefore a larger upper bound is expected. We will also show that a connected cubic graph G of order n ⩾ 8 satisfies i ( G ) ⩽ 2 n /5, providing a new upper bound for cubic graphs.
35009889
Tree Domination in Graphs
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.
44943196
Design for a Learner-Oriented Tracking
Learning Management Systems (LMS) in e-learning have functionality for monitoring learning activities. The statistics generated from learning performances can be processed for tutors and a group of learners to improve their quality of teaching and learning. However the current LMS are not designed to facilitate personalised learning support for an individual learner, e.g. adaptive delivery, constructive feedback on assessment and real-time learning activities monitoring. This paper presents a learner-oriented tracking approach for one-to-one support. Technical components of this approach can be embedded in the LMS to effectively facilitate learning experience of the individual learner and quality of learning content design. A learner-oriented tracking model relies on the information from a Learner’s Profile and educational requirements. This determines initially suitable learning content (learning objects) and delivery methods and also provides monitoring information about learners’ experiences.
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.
206587707
A Design for Generating Personalised Feedback in Knowledge Construction
As the learning paradigm shifts to a more personalised learning process, users need dynamic feedback from their knowledge path. Learning Management Systems (LMS) offer customised feedback dependent on questions and the answers given. However these LMSs are not designed to generate personalised feedback for an individual learner, tutor and instructional designer. This paper presents an approach for generating constructive feedback for all stakeholders during a personalised learning process. 
 
The dynamic personalised feedback model generates feedback based on the learning objectives for the Learning Object. Feedback can be generated at Learning Object level and the Information Object level for both the individual learner and the group. The group feedback is meant for the tutors and instructional designer to improve the learning process.