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Explorations in Algebraic Graph Theory with Sage
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• Title: Explorations in Algebraic Graph Theory with Sage
• Authors Chris Godsil and Rob Beezer
• Publisher: University of Puget Sound
• Paperback: N/A
• eBook: HTML and PDF
• Language: English
• ISBN-10: N/A
• ISBN-13: N/A

Book Description

Algebraic Graph Theory is a beautiful subject and Sage is an ideal place to experiment with the relevant mathematics: graph theory, linear algebra and permutation groups, along with combinatorics generally. This book will provide a useful introduction for the student or researcher, while simultaneously aiding the continual improvement of Sage itself.

This book aims to express properties of graphs in algebraic terms, then to deduce theorems about them. It tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth.

Many algebraists associated a graph with a ring and study the interplay between the structure of the ring and the graph theoretic properties of the graph associated with it. In this book we studied the interplay between ring theoretic properties of a ring and the graph theoretic properties of its comaximal graph, comaximal ideal graph, unit graph and some other graphs related to its comaximal graph and comaximal ideal graph.

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