03723nam 22006255 450 991029998330332120200702194253.01-4471-6569-110.1007/978-1-4471-6569-9(CKB)3710000000249652(Springer)9781447165699(MH)014199315-4(SSID)ssj0001354144(PQKBManifestationID)11868612(PQKBTitleCode)TC0001354144(PQKBWorkID)11322891(PQKB)11338464(DE-He213)978-1-4471-6569-9(MiAaPQ)EBC5588063(Au-PeEL)EBL5588063(OCoLC)891931317(PPN)181352982(EXLCZ)99371000000024965220140919d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierGraphs and Matrices /by Ravindra B. Bapat2nd ed. 2014.London :Springer London :Imprint: Springer,2014.1 online resource (XI, 193 p. 32 illus.)online resourceUniversitext,0172-5939Bibliographic Level Mode of Issuance: Monograph1-4471-6568-3 Preliminaries -- Incidence Matrix -- Adjacency Matrix -- Laplacian Matrix -- Cycles and Cuts -- Regular Graphs -- Line Graph of a Tree -- Algebraic Connectivity -- Distance Matrix of a Tree -- Resistance Distance -- Laplacian Eigenvalues of Threshold Graphs -- Positive Definite Completion Problem -- Matrix Games Based on Graphs.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.Universitext,0172-5939Matrix theoryAlgebraLinear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Matrix theory.Algebra.Linear and Multilinear Algebras, Matrix Theory.512.5Bapat Ravindra Bauthttp://id.loc.gov/vocabulary/relators/aut147505MiAaPQMiAaPQMiAaPQBOOK9910299983303321Graphs and matrices766815UNINAThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress