Graphs and Matrices by Ravindra B. Bapat.
Whilst it is a moot point amongst researchers, linear algebra is an important component in the study of graphs. This book illustrates the elegance and power of matrix techniques in the study of graphs by means of several results, both classical and recent. The emphasis on matrix techniques is greate...
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Format:  eBook 
Language:  English 
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London :
Springer London : Imprint: Springer,
2010.

Edition:  1st ed. 2010. 
Series:  Universitext,
Springer eBook Collection. 
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Online Access:  Click to view ebook 
Holy Cross Note:  Loaded electronically. Electronic access restricted to members of the Holy Cross Community. 
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505  0  a 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.  
520  a Whilst it is a moot point amongst researchers, linear algebra is an important component in the study of graphs. This book illustrates the elegance and power of matrix techniques in the study of graphs by means of several results, both classical and recent. The emphasis on matrix techniques is greater than other standard references on algebraic graph theory, and the important matrices associated with graphs such as incidence, adjacency and Laplacian matrices are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration, and the inclusion of exercises enables practical learning throughout the book. It may also be applied to a selection of subdisciplines within science and engineering. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory who want to be acquainted with matrix theoretic ideas used in graph theory, it will also benefit a wider, crossdisciplinary readership.  
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