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.
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.
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).
40923560
On a problem of J. Csima
Abstract A problem of J. Csima on the factorization of regular bipartite graphs is settled.
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
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.
62228274
Norm-Based Agency for Designing Collaborative Information Systems
Information systems are organizations in which signs are created, processed and consumed. In order to fulfil the organizational goals and objec- tives, its members must understand their responsibilities and authorities, and must act co-operatively. The key to this organization and co-ordination lies in norms, which define responsibilities and authorities for each human agent, and estab- lish regularities of behaviour. In the context of co-operative work, where 'intelli- gent' software agents are involved, to understand the norms of behaviour of various human agents becomes critical. Software agents can perform some tasks autonomously on the user's behalf. Such delegation involves a set of complicated philosophical and legal issues. After discussion on delineation of various bound- aries of responsibility and authorities, this paper addresses norms and normative behaviour of human agents within an organization. It discusses the taxonomies of norms and a method of norm specification, with examples. Finally it presents an approach of norm-based agency for designing collaborative information systems and a case study of an insurance claim for illustration.
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.