The study of directed graphs (digraphs) has developed enormously over recent decades, yet the results are rather scattered across the journal literature. This is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, the authors discuss a large number of applications and their generalizations to topics such as the traveling salesman problem, project scheduling, genetics, network connectivity, and sparse matrices. Numerous exercises are included. For all graduate students, researchers and professionals interested in graph theory and its applications, this book will be essential reading.

Substantially revised, reorganised and updated, the second edition 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.

"When consonants team up they can do many things. Some blend their sounds together. Some make new sounds. These consonant blends and digraphs can be used to build simple words we use every day. Readers learn what these consonant teams can do."--

Facilitate a love of language in students in grades 1–2 with Little Books of Blends and Digraphs! This 64-page book includes 31 eight-page reproducible stories. These humorous, predictable stories cover 20 beginning blends, 7 final blends, and 4 digraphs. The book includes word lists, pre- and post-reading activities, and language arts activities for each story. The book also supports NCTE and NAEYC standards.

Uses wacky sentences and colorful art to teach long vowel sounds and consonant digraphs.

Each of the eight centers in this book contains:sets of a two-sided mat and corresponding task card,reproducible activity pagesPractice It! and Read It!for written practice and assessment,cards presenting words with the targeted letter-sound pattern,answer key, and student record forms

In the present era dominated by computers, graph theory has come into its own as an area of mathematics, prominent for both its theory and its applications. One of the richest and most studied types of graph structures is that of the line graph, where the focus is more on the edges of a graph than on the vertices. A subject worthy of exploration in itself, line graphs are closely connected to other areas of mathematics and computer science. This book is unique in its extensive coverage of many areas of graph theory applicable to line graphs. The book has three parts. Part I covers line graphs and their properties, while Part II looks at features that apply specifically to directed graphs, and Part III presents generalizations and variations of both line graphs and line digraphs. Line Graphs and Line Digraphs is the first comprehensive monograph on the topic. With minimal prerequisites, the book is accessible to most mathematicians and computer scientists who have had an introduction graph theory, and will be a valuable reference for researchers working in graph theory and related fields.