Covering Walks In Graphs
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Covering Walks In Graphs
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Author : Futaba Fujie
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-25
Covering Walks In Graphs written by Futaba Fujie and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-25 with Mathematics categories.
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.
Bounding The Edge Cover Time Of Random Walks On Graphs
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Author : Eric R. Bussian
language : en
Publisher:
Release Date : 1996-06-01
Bounding The Edge Cover Time Of Random Walks On Graphs written by Eric R. Bussian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-01 with Graphic methods categories.
In recent years a great deal of attention has been focused on answering questions regarding the cover times of random walks on simple graphs. In this dissertation we answer questions about the edge cover time of such walks. We begin by reviewing many of the definitions and established results for vertex cover time. We present the little that has been published regarding bounds on the edge cover time. Having completed this review we establish a new, and sometimes more useful, global upper bound for edge cover time. We then narrow our focus and consider the edge cover time of the path. We establish an exact description of the edge cover time for a random walk on the path started at an endpoint in terms of coefficients related to the Bernoulli Numbers of the Second Kind. Studying these coefficients carefully allows us to develop a tight bound on this cover time of (n-1)sq+(Theta)(n-sq/logn). Using these results, and generalizing, provides a description of the edge cover time for walks on the path started from an arbitrary vertex. This generalization gives us a bound of (5/4)(n - 1)sq + O(n-sq/log n) for the edge cover time for the path. Having established a tight bound for walks on paths we then focus on other trees. We prove that the edge cover time for a random walk started from the center of a star graph minimizes edge cover time for walks on all trees on n vertices. We also establish the fact that in all graphs the edge cover time for a walk started from a leaf is always greater than for a walk started from its point of attachment. We continue our study of trees by establishing a global upper bound on the edge cover time for all trees and use it to study balanced k-ary trees. Finally we show the connection between our previous developments for the edge cover time for paths and that of the edge cover time on the cycle.
Discrete Quantum Walks On Graphs And Digraphs
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Author : Chris Godsil
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-31
Discrete Quantum Walks On Graphs And Digraphs written by Chris Godsil and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-31 with Computers categories.
Explore the mathematics arising from discrete quantum walks in this introduction to a rapidly developing area.
Eulerian Graphs And Related Topics
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Author :
language : en
Publisher: Elsevier
Release Date : 1991-06-03
Eulerian Graphs And Related Topics written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-03 with Mathematics categories.
Eulerian Graphs and Related Topics
Random Walks On Infinite Graphs And Groups
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Author : Wolfgang Woess
language : en
Publisher: Cambridge University Press
Release Date : 2000-02-13
Random Walks On Infinite Graphs And Groups written by Wolfgang Woess and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-13 with Mathematics categories.
The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
Algorithms And Computation
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Author : Rudolf Fleischer
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-12-03
Algorithms And Computation written by Rudolf Fleischer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-03 with Computers categories.
This book constitutes the refereed proceedings of the 15th International Symposium on Algorithms and Computation, ISAAC 2004, held in Hong Kong, China in December 2004. The 76 revised full papers presented were carefully reviewed and selected from 226 submissions. Among the topics addressed are computational geometry, graph computations, computational combinatorics, combinatorial optimization, computational complexity, scheduling, distributed algorithms, parallel algorithms, data structures, network optimization, randomized algorithms, and computational mathematics more generally.
Combinatorics Paul Erd S Is Eighty
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Author : Paul Erdős
language : en
Publisher:
Release Date : 1993
Combinatorics Paul Erd S Is Eighty written by Paul Erdős and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Combinatorial analysis categories.
Graphs And Algorithms In Communication Networks
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Author : Arie Koster
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-01
Graphs And Algorithms In Communication Networks written by Arie Koster and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-01 with Computers categories.
Algorithmic discrete mathematics plays a key role in the development of information and communication technologies, and methods that arise in computer science, mathematics and operations research – in particular in algorithms, computational complexity, distributed computing and optimization – are vital to modern services such as mobile telephony, online banking and VoIP. This book examines communication networking from a mathematical viewpoint. The contributing authors took part in the European COST action 293 – a four-year program of multidisciplinary research on this subject. In this book they offer introductory overviews and state-of-the-art assessments of current and future research in the fields of broadband, optical, wireless and ad hoc networks. Particular topics of interest are design, optimization, robustness and energy consumption. The book will be of interest to graduate students, researchers and practitioners in the areas of networking, theoretical computer science, operations research, distributed computing and mathematics.
Graph Theory And Its Applications Second Edition
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Author : Jonathan L. Gross
language : en
Publisher: CRC Press
Release Date : 2005-09-22
Graph Theory And Its Applications Second Edition written by Jonathan L. Gross and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-22 with Mathematics categories.
Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come. The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine. What else is new? New chapters on measurement and analytic graph theory Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing. Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
Arc Routing
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Author : Moshe Dror
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Arc Routing written by Moshe Dror and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
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.