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Graphs and Matrices

by Bapat, R. B.
Material type: materialTypeLabelBookSeries: Universitext: Publisher: New Delhi: Hindustan Book Agency, 2014Edition: 2nd ed.Description: ix, 193 p. : ill. ; 25 cm.ISBN: 9789380250694 (pbk.).Subject(s): Graph theory | Matrices | Graphentheorie | MathematicsDDC classification: 511.5 B228G2 Online resources: Inhaltsverzeichnis
Contents:
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.
Summary: 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.
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General Section
511.5 B228G2 (Browse shelf) Available 7156
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511.35 Si7I3 Introduction to the theory of computation 511.352 W38C Computability Theory 511.36 B388A The Art of Proof : 511.5 B228G2 Graphs and Matrices 511.5 B64G Graph theory 511.5 B799S Spectra of Graphs 511.5 D44G Graph theory with applications to engineering and computer science

Includes bibliographical references (p. 165-168) and index.

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.

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.

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