45781537
Lower bounds on the signed k-subdomination number of graphs
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.
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.
35009889
Tree Domination in Graphs
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.
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).
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].
6235535
Articulation of Learners Requirements for Personalised Instructional Design in e-Learning Services
As e-Learning environments evolve, learners have become increasingly demanding on personalised learning which allows them to build their own knowledge pathway. This significant change in learning requirements imposes a new learning paradigm which ensures one-to-one learning with flexible mode of content configuration, and adaptive delivery and assessment. Although in the past years, Learning Management Systems (LMS) providers have upgraded system functionality to support instructional design for e-learning package, incorporating individual learners’ personal learning requirements in content design still remains challenging. To involve learners in the content design requires identification of their personal learning requirements. This paper presents a method for articulating individual learners’ learning requirements (e.g., learning styles, and prior knowledge), and representing them in a set of computable parameters in Learner’s Profile. These parameters will then be mapped onto instructional design strategies which determine a selection of suitable learning content and sequencing of content with adequate instruction in a learning package.
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.
36070686
Modelling dynamic behaviour of business organisations - extension of DEMO from a semiotic perspective
An organisation is by virtue an information system, in which information is used for communication and coordination of activities. This information system is built upon the organisational infrastructure and is supposed to support the business processes. To study the organisational behaviour in the form of business processes, one needs an effective modelling method to capture dynamics of business processes. In this paper we introduce the DEMO methodology for organisational modelling. An extension of the methodology has been made by incorporating a semiotic method. DEMO is a cross-disciplinary theory for describing and explaining the action of organisations. It contains several model types, each expressed in a specific diagram. They collectively provide the necessary knowledge for information systems development and business process redesign. The process model of DEMO has been discussed in detail in this paper. A need for a facility in DEMO has been identified to formulize rules and conditions for optional and conditional actions. Towards this end, a semiotic method, namely NAM has been chosen as a complement to DEMO for this purpose. After producing process model in terms of DEMO, we use NAM to capture norms (e.g. rules, regulations and conditions). The norms determine the conditions and constrains in controlling optional and conditional actions. They govern the behaviour of actors (agents), normally to decide when certain actions are performed. Norms define clearly the roles, functions, responsibilities and authorities of the actors. The extended DEMO has been applied to a real-life problem for demonstration purposes.
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.