This book presents in a unified and concrete way the beautiful and deep mathematics - both theoretical and computational - on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in the literature. Some results are hidden behind a number of routines in software packages, like Magma and Maple; professional mathematicians very often use these routines just as a black-box, having little idea about the mathematical treasure behind them. Almost 20 years have passed since the first publications on the explicit...

Generalized network design is a very hot topic of research. The monograph describes in a unified manner a series of mathematical models, methods, propositions, and algorithms developed in the last years on generalized network design problems. The book consists of seven chapters, where in addition to an introductory chapter, a number of six generalized network design problems are formulated and examined. The book will be useful for researchers and graduate students interested in operations research, optimization, applied mathematics, and computer science. Due to the substantial practical...

Written for mathematicians working with the theory of graph spectra, this (primarily theoretical) book presents relevant results considering the spectral properties of regular graphs. The book begins with a short introduction including necessary terminology and notation. The author then proceeds with basic properties, specific subclasses of regular graphs (like distance-regular graphs, strongly regular graphs, various designs or expanders) and determining particular regular graphs. Each chapter contains detailed proofs, discussions, comparisons, examples, exercises and also indicates...