Graphs and Matrices

• Preliminaries.- Incidence Matrix.- Adjacency Matrix.- Laplacian Matrix.- Cycles and Cuts.- Regular Graphs.- Algebraic Connectivity.- Distance Matrix of a Tree.- Resistance Distance.- Laplacian Eigenvalues of Threshold Graphs.- Positive Definite Completion Problem.- Matrix Games Based on Graphs.- Hints and Solutions to Selected Exercises.

From the reviews: "Students who have completed introductory courses in linear algebra and graph theory should be able to understand and benefit from this book. It is divided into 12 chapters. ... Each chapter includes ... a good number of references in a bibliographic format. ... A complete bibliography with all of the chapter references is available at the end of the book. Summing Up: Recommended. Upper-division undergraduates through researchers/faculty." (J. T. Saccoman, Choice, Vol. 49 (1), September, 2011) "The book is a study of matrices associated to graphs based on linear algebra techniques. ... The exposition is exact and clear. The proofs are presented in detail and should be understood with no difficulty by any reader with a preliminary background in linear algebra. ... Hence, the book can be used as a textbook for undergraduate level courses. Graduate students and researchers working on spectral graph theory or closely related fields will also benefit from the book." (Behruz Tayfeh-Rezaie, Mathematical Reviews, Issue 2012 f) "A student having completed introductory courses in Linear Algebra and Graph Theory should be able to understand and benefit from this text. At the end of each of the twelve chapters there are a few exercises and a good number of references. ... this text would be a fine resource for an advanced undergraduate or someone wishing to learn more about this synergistic field of study." (John T. Saccoman, The Mathematical Association of America, June, 2011)