Covering Walks in Graphs
Covering Walks in Graphs

Author: Futaba Fujie

Publisher: Springer Science & Business Media

Published: 2014-01-25

Total Pages: 123

ISBN-13: 1493903055

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Covering Walks in Graphs is aimed at researchers and graduate students in the graph theory community and provides a comprehensive treatment on measures of two well studied graphical properties, namely Hamiltonicity and traversability in graphs. This text looks into the famous Kӧnigsberg Bridge Problem, the Chinese Postman Problem, the Icosian Game and the Traveling Salesman Problem as well as well-known mathematicians who were involved in these problems. The concepts of different spanning walks with examples and present classical results on Hamiltonian numbers and upper Hamiltonian numbers of graphs are described; in some cases, the authors provide proofs of these results to illustrate the beauty and complexity of this area of research. Two new concepts of traceable numbers of graphs and traceable numbers of vertices of a graph which were inspired by and closely related to Hamiltonian numbers are introduced. Results are illustrated on these two concepts and the relationship between traceable concepts and Hamiltonian concepts are examined. Describes several variations of traceable numbers, which provide new frame works for several well-known Hamiltonian concepts and produce interesting new results.

Covering Times for Random Walks on Graphs
Covering Times for Random Walks on Graphs

Author: Amine Mohammed Sbihi

Publisher:

Published: 1990

Total Pages: 154

ISBN-13:

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"This thesis is a contribution to the covering times problems for random walks on graphs. By considering uniform random walks on finite connected graphs, the covering time is defined as the time (number of steps) taken by the random walk to visit every vertex. The motivating problem of this thesis is to find bounds for the expected covering times. We provide explicit bounds that are uniformly valid over all starting points and over large classes of graphs. In some cases the asymptotic distribution of the suitably normalized covering time is given as well." --

Random Walks and Electric Networks
Random Walks and Electric Networks

Author: Peter G. Doyle

Publisher: American Mathematical Soc.

Published: 1984-12-31

Total Pages: 159

ISBN-13: 1614440220

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Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.

Handbook of Graph Theory
Handbook of Graph Theory

Author: Jonathan L. Gross

Publisher: CRC Press

Published: 2013-12-17

Total Pages: 1606

ISBN-13: 1439880190

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In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition-over 400 pages longer than its prede

Arc Routing
Arc Routing

Author: Moshe Dror

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 497

ISBN-13: 1461544955

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Arc Routing: Theory, Solutions and Applications is about arc traversal and the wide variety of arc routing problems, which has had its foundations in the modern graph theory work of Leonhard Euler. Arc routing methods and computation has become a fundamental optimization concept in operations research and has numerous applications in transportation, telecommunications, manufacturing, the Internet, and many other areas of modern life. The book draws from a variety of sources including the traveling salesman problem (TSP) and graph theory, which are used and studied by operations research, engineers, computer scientists, and mathematicians. In the last ten years or so, there has been extensive coverage of arc routing problems in the research literature, especially from a graph theory perspective; however, the field has not had the benefit of a uniform, systematic treatment. With this book, there is now a single volume that focuses on state-of-the-art exposition of arc routing problems, that explores its graph theoretical foundations, and that presents a number of solution methodologies in a variety of application settings. Moshe Dror has succeeded in working with an elite group of ARC routing scholars to develop the highest quality treatment of the current state-of-the-art in arc routing.