28317923
Characterization of graphs with equal domination and connected domination numbers
Arumugam and Paulraj Joseph (Discrete Math 206 (1999) 45) have characterized trees, unicyclic graphs and cubic graphs with equal domination and connected domination numbers. In this paper, we extend their results and characterize the class of block graphs and cactus graphs for which the domination number is equal to the connected domination number.
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.
36018188
A note on graphs with largest total k-domination number
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.
428956
On a generalization of signed total dominating functions of 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].
6044165
Articulation of information requirements for personalised knowledge construction
The quality of information provision influences considerably knowledge construction driven by individual users’ needs. In the design of information systems for e-learning, personal information requirements should be incorporated to determine a selection of suitable learning content, instructive sequencing for learning content, and effective presentation of learning content. This is considered as an important part of instructional design for a personalised information package. The current research reveals that there is a lack of means by which individual users’ information requirements can be effectively incorporated to support personal knowledge construction. This paper presents a method which enables an articulation of users’ requirements based on the rooted learning theories and requirements engineering paradigms. The user’s information requirements can be systematically encapsulated in a user profile (i.e. user requirements space), and further transformed onto instructional design specifications (i.e. information space). These two spaces allow the discovering of information requirements patterns for self-maintaining and self-adapting personalisation that enhance experience in the knowledge construction process.
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.
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.
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.