Data Mining Practical Machine Learning Tools and Techniques

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

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A Dynamic Survey of Graph Labeling

The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Digraphs Theory Algorithms And Applications

DNA sequencing with chain terminating inhibitors

Distance-Regular Graphs

The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. General upper bounds - called Moore bounds - for the order of such graphs and digraphs are attainable only for certain special graphs and digraphs. Finding better (tighter) upper bounds for the maximum possible number of vertices, given the other two parameters, and thus attacking the degree/diameter problem 'from above', remains a largely unexplored area. Constructions producing large graphs and digraphs of given degree and diameter represent a way of attacking the degree/diameter problem 'from below'. This survey aims to give an overview of the current state-of-the-art of the degree/diameter problem. We focus mainly on the above two streams of research. However, we could not resist mentioning also results on various related problems. These include considering Moore-like bounds for special types of graphs and digraphs, such as vertex-transitive, Cayley, planar, bipartite, and many others, on the one hand, and related properties such as connectivity, regularity, and surface embeddability, on the other hand.

Moore Graphs and Beyond: A survey of the Degree/Diameter Problem

On irregular total labellings

The `EXACT3D' positron tomograph, which is now in routine clinical research use, was developed with the aim of achieving unprecedented sensitivity, high spatial and temporal resolution and simplicity of design using proven detector technology. It consists of six rings of standard detector blocks (CTI/Siemens EXACT HR+) with 4.39 mm × 4.05 mm × 30 mm elements, giving an axial field of view (FOV) of 23.4 cm. This extended FOV and the absence of interplane septa and retractable transmission rod sources has allowed greatly simplified gantry and detector cassette design. Operation in exclusive 3D mode requires an alternative to the conventional coincidence method for transmission scanning, and a single photon approach using a hydraulically driven 137Cs point source has been implemented. The tomograph has no other moving parts. A single time frame of data without any compression is very large (>300 Mbyte) and two approaches are employed to overcome this difficulty: (a) adjacent sinograms can be summed automatically into different combinations and (b) listmode (event-by-event) acquisition has been instituted, which is both storage efficient (particularly for acquisition of sparse data sets) and maximizes temporal resolution. The high-speed I/O and computing hardware can maintain a sustained acquisition rate of about 4 million coincidence events per second. A disadvantage of the large axial FOV in 3D is the increased sensitivity to activity outside the coincidence FOV. However, this can be minimized by additional side shielding. The mean spatial resolution is 4.8±0.2 mm FWHM (transaxial, 1 cm off-axis) and 5.6±0.5 mm (axial, on-axis). Its absolute efficiency is 5.8% for a line source in air (just spanning the axial FOV) and 10% for a central point source (with thresholds of 350-650 keV). For a uniform 20 cm diameter cylinder, the efficiency is 69 kcps kBq-1 ml-1 (after subtraction of a scatter fraction of 42%). Sensitivity relative to the EXACT HR+ (with four rings of blocks) is 2.5 (3D) and 12 (2D) times respectively. The rate of random events in blood flow studies in the brain and body, using 15O-labelled water, can be controlled by limiting the administered dose and inserting additional side shielding.

Physical characteristics of the ECAT EXACT3D positron tomograph.

A Note on Large Graphs of Diameter Two and Given Maximum Degree

A vertex-magic total labeling of a graph with $v$ vertices and $e$ edges is defined as a one-to-one map taking the vertices and edges onto the integers $1, 2, . . . , v+e$ 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 vertex.
Properties of these labelings are studied. It is shown how to construct labelings for several families of graphs, including cycles, paths, complete graphs of odd order and the complete bipartite graph $K_n,n$. It is also shown that labelings are impossible for some other classes of graphs.

Mirka Miller

Papers

Moore Graphs and Beyond: A survey of the Degree/Diameter Problem

On irregular total labellings

Physical characteristics of the ECAT EXACT3D positron tomograph.

A Note on Large Graphs of Diameter Two and Given Maximum Degree

Vertex-Magic Total Labelings of Graphs