T. Asir

Designed for undergraduate students of computer science, mathematics, and engineering, this book provides the tools and understanding needed to master graph theory and algorithms. It offers a strong theoretical foundation, detailed pseudocodes, and a range of real-world and illustrative examples to bridge the gap between abstract concepts and practical applications. Clear explanations and chapter-wise exercises support ease of comprehension for learners. The text begins with the basic properties of graphs and progresses to topics such as trees, connectivity, and distances in graphs. It also covers Eulerian and Hamiltonian graphs, matchings, planar graphs, and graph colouring. The book concludes with discussions on independent sets, the Ramsey theorem, directed graphs and networks. Concepts are introduced in a structured manner, with appropriate context and support from mathematical language and diagrams. Algorithms are explained through rules, reasoning, pseudocode, and relevant examples.

This book gives an overview of research on graphs associated with commutative rings. The study of the connections between algebraic structures and certain graphs, especially finite groups and their Cayley graphs, is a classical subject which has attracted a lot of interest. More recently, attention has focused on graphs constructed from commutative rings, a field of study which has generated an extensive amount of research over the last three decades. The aim of this text is to consolidate this large body of work into a single volume, with the intention of encouraging interdisciplinary research between algebraists and graph theorists, using the tools of one subject to solve the problems of the other. The topics covered include the graphical and topological properties of zero-divisor graphs, total graphs and their transformations, and other graphs associated with rings. The book will be of interest to researchers in commutative algebra and graph theory and anyone interested in learning about the connections between these two subjects.

This book gives an overview of research on graphs associated with commutative rings. The study of the connections between algebraic structures and certain graphs, especially finite groups and their Cayley graphs, is a classical subject which has attracted a lot of interest. More recently, attention has focused on graphs constructed from commutative rings, a field of study which has generated an extensive amount of research over the last three decades. The aim of this text is to consolidate this large body of work into a single volume, with the intention of encouraging interdisciplinary research between algebraists and graph theorists, using the tools of one subject to solve the problems of the other. The topics covered include the graphical and topological properties of zero-divisor graphs, total graphs and their transformations, and other graphs associated with rings. The book will be of interest to researchers in commutative algebra and graph theory and anyone interested in learning about the connections between these two subjects.