Mod sum number of wheels

title: On d-antimagic labelings of prisms

title: Bounds on the number of isolates in sum graph labeling
abstract: A simple undirected graph H is called a sum graph if there is a labeling L of the vertices of H into distinct positive integers such that any two vertices u and v of H are adjacent if and only if there is a vertex w with label L(w )= L(u )+ L(v). The sum number � (G) of a graph G =( V; E) is the least integer r such that the graph H consisting of G and r isolated vertices is a sum graph. It is clear that � (G)6|E|. In this paper, we discuss general upper and lower bounds on the sum number. In particular, we prove that, over all graphs G =( V; E) with 5xed |V |?3 and |E|, the average of � (G) is at least |E |− 3|V |(log|V |)=[log(( |V | 2 )=|E|)] −| V |− 1. In other words, for most graphs, � (G) ∈ (|E|).

title: Connected graphs which are not mod sum graphs
abstract: In this paper we prove that no wheel with the exception of W 4 can be a mod sum graph. We also give the unique (up to multiplication by positive integers) mod sum labelling of W 4 . We also prove that the symmetric complete bipartite graph K n . n is not a mod sum graph.

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: Large deformation diffeomorphic metric mapping of vector fields
abstract: This paper proposes a method to match diffusion tensor magnetic resonance images (DT-MRIs) through the large deformation diffeomorphic metric mapping of vector fields, focusing on the fiber orientations, considered as unit vector fields on the image volume. We study a suitable action of diffeomorphisms on such vector fields, and provide an extension of the Large Deformation Diffeomorphic Metric Mapping framework to this type of dataset, resulting in optimizing for geodesics on the space of diffeomorphisms connecting two images. Existence of the minimizers under smoothness assumptions on the compared vector fields is proved, and coarse to fine hierarchical strategies are detailed, to reduce both ambiguities and computation load. This is illustrated by numerical experiments on DT-MRI heart images.

title: Dynamic Programming Generation of Curves on Brain Surfaces
abstract: Dynamic programming algorithms are presented for automated generation of length minimizing geodesics and curves of extremal curvature on the neocortex of the macaque and the visible human. Probabilistic models of curve variation are constructed in terms of the variability in speed, curvature, and torsion in the Frenet representation.

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=

title: Information measures for object recognition accommodating signature variability
abstract: This paper presents measures characterizing the information content of remote observations of ground scenes imaged via optical and infrared sensors. Object recognition is posed in the context of deformable templates; the special Euclidean group is used to accommodate geometric variation of object pose. Principal component analysis of object signatures is used to represent and efficiently accommodate variation in object signature due to changes in the thermal state of the object surface. Mutual information measures, which are independent of the recognition system, are calculated quantifying both the information gain due to remote observations of the scene and the information loss due to signature variability. Signature model mismatch is quantitatively examined using the Kullback-Leibler divergence. Expressions are derived quadratically approximating the posterior conditional entropy on the orthogonal group for high signal-to-noise ratio. It is demonstrated that quadratic modules accurately characterize the posterior entropy for broad ranges of signal-to-mise ratio. Information gain in multiple-sensor scenarios is quantified, and it is demonstrated that the cost of signature uncertainty for the Comanche series of FLIR images collected by the US Army Night Vision Electronic Sensors Directorate is approximately 0.8 bits with an associated near doubling of mean-squared error uncertainty in pose.

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.