## ＜電子ブック＞Graphs and Matrices

責任表示 by Ravindra B. Bapat Bapat, Ravindra B SpringerLink (Online service) 2nd ed. 2014. English (英語) Springer London Imprint: Springer 2014- London, United Kingdom シリーズ Universitext 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 associat...ed 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.続きを見る PreliminariesIncidence MatrixAdjacency MatrixLaplacian MatrixCycles and CutsRegular GraphsLine Graph of a TreeAlgebraic ConnectivityDistance Matrix of a TreeResistance DistanceLaplacian Eigenvalues of Threshold GraphsPositive Definite Completion ProblemMatrix Games Based on Graphs.続きを見る http://hdl.handle.net/2324/1001547248 Full text available from Springer Mathematics and Statistics eBooks 2014 English/International

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レコードID 3331285 QA184-205 512.5 Matrix theory. Linear and Multilinear Algebras, Matrix Theory. ssj0001354144 9781447165705[1447165705](print) 9781447165682[1447165683](print) 9781447165699[1447165691] 2020.06.27 2020.06.28