41148524
Vertex-Magic Total Labelings Of Generalized Petersen Graphs
A vertex-magic total labeling of a graph G=(V, E) with v vertices and e edges is an assignment of the integers from 1 to v + e to the vertices and edges of G with the property that the sum of the label on a vertex and the labels on its incident edges is a constant, independent of the choice of the vertex. In this paper we give a vertex-magic total labeling for the generalized Petersen graphs P(n, m) for all n@3,1@m⌊(n−1)/2⌋.
30156520
Mod sum number of wheels
2423429
On d-antimagic labelings of prisms
33503104
Almost Moore digraphs are diregular
Abstract An almost Moore digraph is a digraph of diameter k⩾2 , maximum out-degree d⩾2 and order n=d+d 2 +⋯+d k , that is, one less than the Moore bound. It is easy to show that the out-degree of an almost Moore digraph is constant (=d) . In this note we prove that also the in-degree of an almost Moore digraph is constant (=d) , that is, every almost Moore digraph is diregular of degree d .
16296646
A Note on Constructing Large Cayley Graphs of Given Degree and Diameter by Voltage Assignments
Voltage graphs are a powerful tool for constructing large graphs (called lifts ) with prescribed properties as covering spaces of small base graphs. This makes them suitable for application to the degree/diameter problem , which is to determine the largest order of a graph with given degree and diameter. Many currently known largest graphs of degree $\le 15$ and diameter $\le 10$ have been found by computer search among Cayley graphs of semidirect products of cyclic groups. We show that all of them can in fact be described as lifts of smaller Cayley graphs of cyclic groups, with voltages in (other) cyclic groups. This opens up a new possible direction in the search for large vertex-transitive graphs of given degree and diameter.
30300287
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.
35339559
Two new families of large compound graphs
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. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 47(3), 140–146 2006
10226081
A MAC protocol to reduce sensor network energy consumption using a wakeup radio
For increasing the life of sensor networks, each node must conserve energy as much as possible. In this paper, we propose a protocol in which energy is conserved by amortizing the energy cost of communication over multiple packets. In addition, we allow sensors to control the amount of buffered packets since storage space is limited. To achieve this, a two-radio architecture is used which allows a sensor to "wakeup" a neighbor with a busy tone and send its packets for that destination. However, this process is expensive because all neighbors must awake and listen to the primary channel to determine who is the intended destination. Therefore, triggered wakeups on the primary channel are proposed to avoid using the more costly wakeup procedure. We present a protocol for efficiently determining how large the period for these wakeups should be such that energy consumption is reduced.
1871640
Exploring the Energy-Latency Trade-Off for Broadcasts in Energy-Saving Sensor Networks
Networking protocols for multi-hop wireless sensor networks (WSNs) are required to simultaneously minimize resource usage as well as optimize performance metrics such as latency and reliability. This paper explores the energy-latency-reliability trade-off for broadcast in multi-hop WSNs, by presenting a new protocol called PBBF (probability-based broadcast forwarding). PBBF works at the MAC layer and can be integrated into any sleep scheduling protocol. For a given application-defined level of reliability for broadcasts, the energy required and latency obtained are found to be inversely related to each other. Our analysis and simulation study quantify this relationship at the reliability boundary, as well as performance numbers to be expected from a deployment. PBBF essentially offers a WSN application designer considerable flexibility in choice of desired operation points
14209020
Volumetric transformation of brain anatomy
Presents diffeomorphic transformations of three-dimensional (3-D) anatomical image data of the macaque occipital lobe and whole brain cryosection imagery and of deep brain structures in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarchical manner, accommodating both global and local anatomical detail. The initial low-dimensional registration is accomplished by constraining the transformation to be in a low-dimensional basis. The basis is defined by the Green's function of the elasticity operator placed at predefined locations in the anatomy and the eigenfunctions of the elasticity operator. The high-dimensional large deformations are vector fields generated via the mismatch between the template and target-image volumes constrained to be the solution of a Navier-Stokes fluid model. As part of this procedure, the Jacobian of the transformation is tracked, insuring the generation of diffeomorphisms. It is shown that transformations constrained by quadratic regularization methods such as the Laplacian, biharmonic, and linear elasticity models, do not ensure that the transformation maintains topology and, therefore, must only be used for coarse global registration.
2078197
Collaborative Agents for C2 Teamwork Simulation
Existing team training software often requires that trainees be organized as physical teams and the members of the same team be trained at the same time. To demonstrate that team training software can be made more flexible, this paper presents an approach to incorporating software agents into the distributed command-and-control (C2) simulation software DDD, which supports only human players. Based on the multi-agent architecture CAST, the software agents are designed as a team to perform C2 tasks in the DDD. By associating the agents with the same basic capabilities as the DDD provides its human users, we illustrate how to specify the teamwork knowledge for the agent team, and how to make agents efficiently reason about the dynamic, partially observable environment. Different methods of communication and coordination among agents are also briefly described.