The history, formulas, and most famous puzzles of graph theoryGraph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. The Fascinating World of Graph Theory explores the ques...

Graphs & Digraphs, Seventh Edition masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. This classic text, widely popular among students and instructors alike for decades, is thoroughly streamlined in this new, seventh edition, to present a text consistent with contemporary expectations.Changes and updates t...

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 variou...

Die Theorie der regularen Graphen (The Theory of Regular Graphs), written by the Danish Mathematician Julius Petersen in 1891, is often considered the first strictly theoretical paper dealing with graphs. In the 130 years since then, regular graphs have been a common and popular area of study. While regular graphs are typically considered to be graphs whose vertices all have the same degree, a more general interpretation is that of graphs possessing some common characteristic throughout th...

This book depicts graph labelings that have led to thought-provoking problems and conjectures. Problems and conjectures in graceful labelings, harmonious labelings, prime labelings, additive labelings, and zonal labelings are introduced with fundamentals, examples, and illustrations. A new labeling with a connection to the four color theorem is described to aid mathematicians to initiate new methods and techniques to study classical coloring problems from a new perspective. Researchers and...

This book is in honor of the 80th birthday of Stephen Hedetniemi. It describes advanced material in graph theory in the areas of domination, coloring, spanning cycles and circuits, and distance that grew out of research topics investigated by Stephen Hedetniemi. The purpose of this book is to provide background and principal results on these topics, along with same related problems and conjectures, for researchers in these areas. The most important features deal with material, results, and...

Digital Control Engineering covers the fundamental principles and applications of digital control engineering, with emphasis on engineering design. Digital controllers are part of nearly all modern personal, industrial, and transportation systems. Every senior or graduate student of electrical, chemical or mechanical engineering should therefore be familiar with the basic theory of digital controllers. This book features Matlab sections at end of each chapter which show how to implement co...

This rigorous tutorial is aimed at both power system professionals and electrical engineering students. Breaking down the complexities of load flow analysis into a series of short, focused chapters, the book develops each of the major algorithms used, covers the handling of generators and transformers in the analysis process, and details how these algorithms can be deployed in powerful software. Having read the book, and EE student or engineer will have all the tools necessary to predict l...

The subject of Digital Signal Processing (DSP) is enormously complex, involving many concepts, probabilities, and signal processing that are woven together in an intricate manner. To cope with this scope and complexity, many DSP texts are often organized around the &quote;numerical examples&quote; of a communication system. With such organization, readers can see through the complexity of DSP, they learn about the distinct concepts and protocols in one part of the communication system whil...

Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics.In each lecture, the concepts, theories and methods are taken as the core. The examples are ser...

The book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also fo...

Need help with your Trig homework? Could you benefit from having quick access to fundamental facts and formulas? The Trigonometry Study Brief is intended as a quick and convenient reference for students enrolled in a basic trigonometry class. It is ideal for any adult learner approaching the study of advanced mathematics who may benefit from a quick refresher on foundational trigonometric topics. This academic outline collects together a wealth of useful examples, formulas and equations in...