Properly Colored Connectivity Of Graphs PDF Download
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Author | : Xueliang Li |
Publisher | : Springer |
Total Pages | : 145 |
Release | : 2018-05-14 |
Genre | : Mathematics |
ISBN | : 3319896172 |
Download Properly Colored Connectivity of Graphs Book in PDF, ePub and Kindle
A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.
Author | : Ping Zhang |
Publisher | : Springer |
Total Pages | : 160 |
Release | : 2016-03-30 |
Genre | : Mathematics |
ISBN | : 3319305182 |
Download A Kaleidoscopic View of Graph Colorings Book in PDF, ePub and Kindle
This book describes kaleidoscopic topics that have developed in the area of graph colorings. Unifying current material on graph coloring, this book describes current information on vertex and edge colorings in graph theory, including harmonious colorings, majestic colorings, kaleidoscopic colorings and binomial colorings. Recently there have been a number of breakthroughs in vertex colorings that give rise to other colorings in a graph, such as graceful labelings of graphs that have been reconsidered under the language of colorings. The topics presented in this book include sample detailed proofs and illustrations, which depicts elements that are often overlooked. This book is ideal for graduate students and researchers in graph theory, as it covers a broad range of topics and makes connections between recent developments and well-known areas in graph theory.
Author | : Ping Zhang |
Publisher | : Springer |
Total Pages | : 130 |
Release | : 2015-08-10 |
Genre | : Mathematics |
ISBN | : 3319203940 |
Download Color-Induced Graph Colorings Book in PDF, ePub and Kindle
A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge coloring and the kind of objects serving as colors, but also on the property demanded of the vertex coloring produced. For each edge coloring introduced, background for the concept is provided, followed by a presentation of results and open questions dealing with this topic. While the edge colorings discussed can be either proper or unrestricted, the resulting vertex colorings are either proper colorings or rainbow colorings. This gives rise to a discussion of irregular colorings, strong colorings, modular colorings, edge-graceful colorings, twin edge colorings and binomial colorings. Since many of the concepts described in this book are relatively recent, the audience for this book is primarily mathematicians interested in learning some new areas of graph colorings as well as researchers and graduate students in the mathematics community, especially the graph theory community.
Author | : Stephen Devereaux |
Publisher | : |
Total Pages | : 112 |
Release | : 2017 |
Genre | : Computers |
ISBN | : |
Download Color-connected Graphs and Information-transfer Paths Book in PDF, ePub and Kindle
The Department of Homeland Security in the United States was created in 2003 in response to weaknesses discovered in the transfer of classified information after the September 11, 2001 terrorist attacks. While information related to national security needs to be protected, there must be procedures in place that permit access between appropriate parties. This two-fold issue can be addressed by assigning information-transfer paths between agencies which may have other agencies as intermediaries while requiring a large enough number of passwords and rewalls that is prohibitive to intruders, yet small enough to manage. Situations such as this can be represented by a graph whose vertices are the agencies and where two vertices are adjacent if there is direct access between them. Such graphs can then be studied by means of certain edge colorings of the graphs, where colors here refer to passwords. During the past decade, many research topics in graph theory have been introduced to deal with this type of problem. In particular, edge colorings of connected graphs have been introduced that deal with various ways every pair of vertices are connected by paths possessing some prescribed color condition. Let G be an edge-colored connected graph, where adjacent edges may be colored the same. A path P is a rainbow path in an edge-colored graph G if no two edges of P are colored the same. An edge coloring c of a connected graph G is a rainbow coloring of G if every pair of distinct vertices of G are connected by a rainbow path in G. In this case, G is rainbow-connected. The minimum number of colors needed for a rainbow coloring of G is referred to as the rainbow connection number of G and is denoted by rc(G). A path P is a proper path in G if no two adjacent edges of P are colored the same. An edge coloring c of a connected graph G is a proper-path coloring of G if every pair of distinct vertices of G are connected by a proper path in G. If k colors are used, then c is referred to as a proper-path k-coloring. The minimum k for which G has a proper-path k-coloring is called the proper connection number pc(G) of G. In recent years, these two concepts have been studied extensively by many researchers. It has been observed that these two concepts model a communications network, where the goal is to transfer information in a secure manner between various law enforcement and intelligence agencies.
Author | : Xueliang Li |
Publisher | : Springer Science & Business Media |
Total Pages | : 108 |
Release | : 2012-02-23 |
Genre | : Mathematics |
ISBN | : 1461431190 |
Download Rainbow Connections of Graphs Book in PDF, ePub and Kindle
Rainbow connections are natural combinatorial measures that are used in applications to secure the transfer of classified information between agencies in communication networks. Rainbow Connections of Graphs covers this new and emerging topic in graph theory and brings together a majority of the results that deal with the concept of rainbow connections, first introduced by Chartrand et al. in 2006. The authors begin with an introduction to rainbow connectedness, rainbow coloring, and rainbow connection number. The work is organized into the following categories, computation of the exact values of the rainbow connection numbers for some special graphs, algorithms and complexity analysis, upper bounds in terms of other graph parameters, rainbow connection for dense and sparse graphs, for some graph classes and graph products, rainbow k-connectivity and k-rainbow index, and, rainbow vertex-connection number. Rainbow Connections of Graphs appeals to researchers and graduate students in the field of graph theory. Conjectures, open problems and questions are given throughout the text with the hope for motivating young graph theorists and graduate students to do further study in this subject.
Author | : Gary Chartrand |
Publisher | : CRC Press |
Total Pages | : 450 |
Release | : 2019-11-28 |
Genre | : Mathematics |
ISBN | : 042979827X |
Download Chromatic Graph Theory Book in PDF, ePub and Kindle
With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition
Author | : Melissa Marie Fuentes |
Publisher | : |
Total Pages | : 80 |
Release | : 2013 |
Genre | : Bipartite graphs |
ISBN | : |
Download Proper Connection of Bipartite Circulant Graphs Book in PDF, ePub and Kindle
Author | : W. T. Tutte |
Publisher | : |
Total Pages | : 164 |
Release | : 1966 |
Genre | : Mathematics |
ISBN | : |
Download Connectivity in Graphs Book in PDF, ePub and Kindle
Author | : Weili Wu |
Publisher | : Springer Nature |
Total Pages | : 505 |
Release | : 2024-01-09 |
Genre | : Computers |
ISBN | : 3031496140 |
Download Combinatorial Optimization and Applications Book in PDF, ePub and Kindle
The two-volume set LNCS 14461 and LNCS 14462 constitutes the refereed proceedings of the 17th International Conference on Combinatorial Optimization and Applications, COCOA 2023, held in Hawaii, HI, USA, during December 15–17, 2023. The 73 full papers included in the proceedings were carefully reviewed and selected from 117 submissions. They were organized in topical sections as follows: Part I: Optimization in graphs; scheduling; set-related optimization; applied optimization and algorithm; Graph planer and others; Part II: Modeling and algorithms; complexity and approximation; combinatorics and computing; optimization and algorithms; extreme graph and others; machine learning, blockchain and others.
Author | : Xiaofeng Gao |
Publisher | : Springer |
Total Pages | : 496 |
Release | : 2017-12-06 |
Genre | : Computers |
ISBN | : 3319711504 |
Download Combinatorial Optimization and Applications Book in PDF, ePub and Kindle
The two-volume set LNCS 10627 and 10628 constitutes the refereed proceedings of the 11th International Conference on Combinatorial Optimization and Applications, COCOA 2017, held in Shanghai, China, in December 2017. The 59 full papers and 19 short papers presented were carefully reviewed and selected from 145 submissions. The papers cover most aspects of theoretical computer science and combinatorics related to computing, including classic combinatorial optimization, geometric optimization, complexity and data structures, and graph theory. They are organized in topical sections on network, approximation algorithm and graph theory, combinatorial optimization, game theory, and applications.