On the sum number of wheels
A graph G=(V,E) is a sum graph if there exists a labelling of the vertices of G with distinct positive integers so that uv∈E if and only if the sum of the labels assigned to u and v is the label of a vertex of G. The sum number of a graph is the minimum number of isolated vertices that, together with the given graph, form a sum graph. Sum graph labellings of wheels have been examined previously by other investigators. The sum number of an n spoked wheel, σ(Wn),n⩾5, has been found to be n when n is odd and n2+2 when n is even; however the proofs of these results are incomplete. In this paper we provide a complete proof and affirm that these previous results are correct.

title: Mod sum number of wheels

title: Digraphs of degree two which miss the Moore bound by two
abstract: It is well known that Moore digraphs do not exist except for trivial cases (degree one or diameter one). Consequently, for a given maximum out-degree d and a given diameter, we wish to find a digraph whose order misses the Moore bound by the smallest possible ‘defect’. For diameter two and arbitrary degree there are digraphs which miss the Moore bound by one. No examples of such digraphs of diameter at least three are known, although several necessary conditions for their existence have been obtained. In the case of degree two, it has been shown that there are no digraphs of diameter greater than two and defect one. There are five nonisomorphic digraphs of degree two, diameter two and defect two. In this paper we prove that digraphs of degree two and diameter k ⩾3 which miss the Moore bound by two do not exist.

title: Characterization of eccentric digraphs
abstract: The eccentric digraphED(G) of a digraph G represents the binary relation, defined on the vertex set of G, of being 'eccentric'; that is, there is an arc from u to v in ED(G) if and only if v is at maximum distance from u in G. A digraph G is said to be eccentric if there exists a digraph H such that G=ED(H). This paper is devoted to the study of the following two questions: what digraphs are eccentric and when the relation of being eccentric is symmetric. We present a characterization of eccentric digraphs, which in the undirected case says that a graph G is eccentric iff its complement graph G@? is either self-centered of radius two or it is the union of complete graphs. As a consequence, we obtain that all trees except those with diameter 3 are eccentric digraphs. We also determine when ED(G) is symmetric in the cases when G is a graph or a digraph that is not strongly connected.

title: Minimum Diameter of Diregular Digraphs of Degree 2
abstract: Etude de certaines relations entre le nombre de sommets, degre et diametre de graphes finis diregulaires. Les trois problemes consideres sont N(d,k), K(u,d) et D(u, k) ou, autrement dit, trouver le nombre maximum possible de sommets etant donnes le degre d et le diametre k; trouver le diametre minimum possible etant donnes le nombre de sommets n et le degre d et trouver le degre minimum possible etant donnes le nombre de sommets n et le diametre k respectivement

title: On d-antimagic labelings of prisms

title: Two new families of large compound graphs
abstract: A question of special interest in graph theory is the design of large graphs. Specifically, we want to find constructions of graphs with order as large as possible for a given degree and diameter D . Two generalizations of two large compound graphs are proposed in this article. Three particular cases of these families of graphs presented here allow us to improve the order for the entries (15, 7), (13, 10), and (15, 10) in the table of the largest known ( , D)-graphs.

title: On the degrees of a strongly vertex-magic graph
abstract: Let G=(V,E) be a finite graph, where |V|=n>=2 and |E|=e>=1. A vertex-magic total labeling is a bijection @l from V@?E to the set of consecutive integers {1,2,...,n+e} with the property that for every v@?V, @l(v)+@?"w"@?"N"("v")@l(vw)=h for some constant h. Such a labeling is strong if @l(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>=10n^2-6n+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.

title: Bayesian Segmentation via Asymptotic Partition Functions
abstract: Asymptotic approximations to the partition function of Gaussian random fields are derived. Textures are characterized via Gaussian random fields induced by stochastic difference equations determined by finitely supported, stationary, linear difference operators, adjusted to be nonstationary at the boundaries. It is shown that as the scale of the underlying shape increases, the log-normalizer converges to the integral of the log-spectrum of the operator inducing the random field. Fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator-induced random field model. Matrix analysis techniques are proposed for handling textures with variable orientation. Examples of texture parameters estimated from training data via asymptotic maximum-likelihood are shown. Isotropic models involving powers of the Laplacian and directional models involving partial derivative mixtures are explored. Parameters are estimated for mitochondria and actin-myocin complexes in electron micrographs and clutter in forward-looking infrared images. Deformable template models are used to infer the shape of mitochondria in electron micrographs, with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds.

title: Training Teams with Collaborative Agents
abstract: Training teams is an activity that is expensive, time-consuming, hazardous in some cases, and can be limited by availability of equipment and personnel. In team training, the focus is on optimizing interactions, such as efficiency of communication, conflict resolution and prioritization, group situation awareness, resource distribution and load balancing, etc. This paper presents an agent-based approach to designing intelligent team training systems. We envision a computer-based training system in which teams are trained by putting them through scenarios, which allow them to practice their team skills. There are two important roles that intelligent agents can play; these are as virtual team members and as coach. To carry out these functions, these agents must be equipped with an understanding of the task domain, the team structure, the selected decision-making process and their belief about other team members' mental states.

title: Consecutive magic graphs
abstract: 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)^2+n^2=(2e+1)^2. Moreover, we show that every tree with even order is not a-vertex consecutive magic and, if a tree of odd order is a-vertex consecutive then a=n-1. Furthermore, we show that every a-vertex consecutive magic graph has minimum degree at least two if a=0, or both 2e>=6n^2-2n+1 and 2a==10n^2-6n+1+4a and 2a=