Springer Graphs from Rings

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. From the Back Cover 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. About the Author David F. Anderson is Professor Emeritus of Mathematics at The University of Tennessee-Knoxville, a Fellow of the American Mathematical Society, and now lives in Murfreesboro, Tennessee. He received his BS degree from Iowa State University in 1971 and PhD from the University of Chicago in 1976. His research interests are in commutative ring theory, particularly in divisibility and (non-unique) factorization in integral domains and associating graphs to commutative rings. He has written numerous research articles on these and related topics. T. Asir is the Assistant Professor and Head at Department of Mathematics-DDE, Madurai Kamaraj University, India. His research interests are in algebraic graph theory and combinatorial commutative algebra. He has published 23 research articles in WoS-SCIE journals. His research work has been supported by various funding agencies like DST, UGC, SERB, CSIR and DSR-Saudi Arabia. He has delivered more than 50 invited talks at various conferences. Also, he has developed online mathematical content through MOOC Courses “Modern Algebra” and “Graph Theory” in SWAYAM-MHRD. Orcid-id: https://orcid.org/0000-0002-9035-6996 Ayman Badawi is a Professor at the Department of Mathematical and Statistical Sciences at the American University of Sharjah, UAE. He holds a Ph.D. in Mathematics from the University of North Texas, Texas, USA. His research interests are in the area of commutative ring theory and graphs associated to rings. Dr. Badawi is the editor in chief of the Palestine Journal of Mathematics (PJM). He has numerous publications, including book chapters, journal articles, and conference proceedings. A complete list of his works can be found on the university webpage: https://www2.aus.edu/facultybios/profile.php?faculty=abadawi   and   www.ayman-badaw