### On the degrees of a strongly vertex-magic graph

**Authors:**Balbuena, Camino , Barker, Ewan , Das, K. C. , Lin, Yuqing , Miller, Mirka , Ryan, Joe , Slamin, , Sugeng, Kiki Ariyanti , Tkac, M.**Date:**2006**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 306, no. 6 (2006), p. 539-551**Full Text:**false**Reviewed:****Description:**Let G=(V,E) be a finite graph, where |V|=n≥2 and |E|=e≥1. A vertex-magic total labeling is a bijection λ from V∪E to the set of consecutive integers {1,2,...,n+e} with the property that for every v∈V, λ(v)+∑w∈N(v)λ(vw)=h for some constant h. Such a labeling is strong if λ(V)={1,2,...,n}. In this paper, we prove first that the minimum degree of a strongly vertex-magic graph is at least two. Next, we show that if 2e≥10n2-6n+1, then the minimum degree of a strongly vertex-magic graph is at least three. Further, we obtain upper and lower bounds of any vertex degree in terms of n and e. As a consequence we show that a strongly vertex-magic graph is maximally edge-connected and hamiltonian if the number of edges is large enough. Finally, we prove that semi-regular bipartite graphs are not strongly vertex-magic graphs, and we provide strongly vertex-magic total labeling of certain families of circulant graphs. © 2006 Elsevier B.V. All rights reserved**Description:**C1**Description:**2003001603

### Consecutive magic graphs

**Authors:**Balbuena, Camino , Barker, Ewan , Lin, Yuqing , Miller, Mirka , Sugeng, Kiki Ariyanti**Date:**2006**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 306, no. 16 (2006), p. 1817-1829**Full Text:**false**Reviewed:****Description:**Let G be a graph of order n and size e. A vertex-magic total labeling is an assignment of the integers 1, 2, ..., n + e to the vertices and the edges of G, so that at each vertex, the vertex label and the labels on the edges incident at that vertex, add to a fixed constant, called the magic number of G. Such a labeling is a-vertex consecutive magic if the set of the labels of the vertices is { a + 1, a + 2, ..., a + n }, and is b-edge consecutive magic if the set of labels of the edges is { b + 1, b + 2, ..., b + e }. In this paper we prove that if an a-vertex consecutive magic graph has isolated vertices then the order and the size satisfy (n - 1)**Description:**C1**Description:**2003001604

### Constructing stochastic mixture policies for episodic multiobjective reinforcement learning tasks

**Authors:**Vamplew, Peter , Dazeley, Richard , Barker, Ewan , Kelarev, Andrei**Date:**2009**Type:**Text , Book chapter**Relation:**AI 2009 : Advances in Artificial Intelligence : 22nd Australasian Joint Conference, Melbourne, Australia, December 1-4, 2009. Proceedings Chapter p. 340-349**Full Text:****Description:**Multiobjective reinforcement learning algorithms extend reinforcement learning techniques to problems with multiple conflicting objectives. This paper discusses the advantages gained from applying stochastic policies to multiobjective tasks and examines a particular form of stochastic policy known as a mixture policy. Two methods are proposed for deriving mixture policies for episodic multiobjective tasks from deterministic base policies found via scalarised reinforcement learning. It is shown that these approaches are an efficient means of identifying solutions which offer a superior match to the user’s preferences than can be achieved by methods based strictly on deterministic policies.**Description:**2003007906

### Changes of names, contents and attitudes to mathematical units

**Authors:**Turville, Christopher , Pierce, Robyn , Barker, Ewan , Giri, Jason**Date:**2002**Type:**Text , Conference paper**Relation:**Paper presented at the 2nd International Conference on the Teaching of Mathematics, Crete, Greece : 1st June, 2003**Full Text:****Reviewed:****Description:**Will this material be on the exam? Why do I need to know this stuff? These are the sorts of questions that have been regularly asked by our mathematics students. Pre-service mathematics teachers often suggest that they do not need to learn anything that they do not have to teach. Generally, these students appear to have very little aesthetic appreciation for mathematics and its applications. Currently, we teach five traditional mathematical content units that are provided mainly for pre-service mathematics teachers. These units have been adapted and modified over the years from units that were designed primarily for science students. They contained a heavy focus on calculus with a limited breadth of mathematical experience. After consulting widely on the best mathematical practices throughout Australia and internationally, it was decided to reform all of the mathematics units to make them more attractive to a wider audience. The units that are currently being developed are: Profit, Loss and Gambling; Upon the Shoulders of Giants; Logic and Imagination; Modelling and Change; Algorithms, Bits and Bytes; Space, Shape, and Design; and Modelling Reality. The overall goal of this redevelopment is to improve student attitudes and motivation by exposing them to a wide range of topics in mathematics that are usable and relevant. All of these units will incorporate current technology, contain realistic problems, and include visiting speakers. Student assessment in these units will consist of portfolios, projects and examinations. The introduction of these new units will result in students having a greater choice of the units they wish to study. In order to overcome potential logistical problems of a small mathematics department, innovative changes to the structure of the units will also be examined. This paper will provide the details of the establishment and content of these units.**Description:**E1**Description:**2003000085