EAN: 9781447165682

UNIVERSITEXT GRAPHS AND MATRICES - RAVINDRA B...

This new edition illustrates the power of linear algebra in the study of graphs. The emphasis
on matrix techniques is greater than in other texts on algebraic graph theory. Important
matrices associated with graphs (for example  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. The inclusion of exercises
enables practical learning throughout the book. In the new edition  a new chapter is added on
the line graph of a tree  while some results in Chapter 6 on Perron-Frobenius theory are
reorganized. Whilst this book will be invaluable to students and researchers in graph theory
and combinatorial matrix theory  it will also benefit readers in the sciences and engineering.

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