Locating Eigenvalues in Graphs

Carlos Hoppen holds a PhD in Combinatorics and Optimization from the University of Waterloo, Canada. He is an Associate Professor of Mathematics at the Federal University of Rio Grande do Sul (UFRGS), Brazil. His research focuses on probabilistic and extremal combinatorics, and spectral graph theory.David P. Jacobs is a Professor Emeritus of Computer Science at Clemson University, USA. He has done research in various areas including graph algorithms and spectral graph theory. In 2006, he visited UFRGS as a Fulbright Scholar.Vilmar Trevisan is a Professor of Mathematics at UFRGS. He earned a PhD in Mathematics at Kent State University, USA. His research focuses on combinatorics and spectral graph theory. He is currently a Visiting Professor at the Università degli Studi di Napoli, Italy.

• Preface.- Introduction.- Preliminaries.- Locating Eigenvalues in Trees.- Graph Representations.- Locating Eigenvalues in Threshold Graphs and Cographs.- Locating Eigenvalues in Arbitrary Graphs.- Locating Eigenvalues in Distance  Hereditary Graphs.- Some Other Algorithms.- References.

“The book is well structured, and gives the necessary background, detailed insight into eigenvalue location algorithms as well as their applications and possible relations with some open problems. It provides a concise and at the same time rich introduction to eigenvalue location algorithms.” (Milica Andelić, zbMATH 1511.05001, 2023)