Graphs from Rings

lt;p>David F. Anderson is Emeritus Professor of Mathematics at the University of Tennessee, Knoxville, Tennessee, USA. His research interests are in commutative ring theory and graphs associated to rings. He has published more than 160 papers in different branches of commutative algebra, many appearing in prestigious journals such as the Proceedings of the American Mathematical Society, Journal of Algebra, Journal of Pure and Applied Algebra, Communications in Algebra, and the Journal of Algebra and Its Applications. Professor Anderson has been a keynote speaker at several American Mathematical Society meetings.

T. Asir is an Assistant Professor in the Department of Mathematics, DDE, Madurai Kamaraj University, Tamil Nadu, India. His research is on graphs constructed from commutative rings and he has a particular interest in their topological properties.

Ayman Badawi is a Professor in the Department of Mathematical and Statistical Sciences at the American University of Sharjah and is the editor in chief of the Palestine Journal of Mathematics. He holds a Ph.D. in mathematics from the University of North Texas. His research interests are in commutative ring theory and graphs associated with rings. He has numerous publications, including book chapters, journal articles, and conference proceedings.

T. Tamizh Chelvam is a Professor of Mathematics at Manonmaniam Sundaranar University, Tamil Nadu, India. His field of specialization is generalized rings and graphs associated with algebraic structures. More specifically, he is interested in problems related to domination in zero-divisor graphs and total graphs constructed from commutative rings. He has also published papers on domination in circulant graphs, a family of Cayley graphs constructed from finite groups.

Introduction.- Distances in zero-divisor graphs.- Properties of zero-divisor graphs.- Genus of zero-divisor graphs.- Zero-divisor graph generalizations.- Total graphs of commutative rings.- Graphs from total graphs.- Generalized total graphs.- Other graphs associated with rings.- Bibliography.- Index.

"This book is really attractive, comprehensive, and full of valuable results for anyone working on the borderline between ring theory and graph theory." (Mehrdad Nasernejad, Mathematical Reviews, April, 2023)

“This book is a very good survey of graphs defined on rings. The authors have collected results on almost all types of graphs related to rings. The book consists of ten chapters and an exhaustive bibliography of 443 items.” (S. K. Nimbhorkar, zbMATH 1486.13001, 2022)