LEADER 03723nam 22006255 450 001 9910299983303321 005 20200702194253.0 010 $a1-4471-6569-1 024 7 $a10.1007/978-1-4471-6569-9 035 $a(CKB)3710000000249652 035 $a(Springer)9781447165699 035 $a(MH)014199315-4 035 $a(SSID)ssj0001354144 035 $a(PQKBManifestationID)11868612 035 $a(PQKBTitleCode)TC0001354144 035 $a(PQKBWorkID)11322891 035 $a(PQKB)11338464 035 $a(DE-He213)978-1-4471-6569-9 035 $a(MiAaPQ)EBC5588063 035 $a(Au-PeEL)EBL5588063 035 $a(OCoLC)891931317 035 $a(PPN)181352982 035 $a(EXLCZ)993710000000249652 100 $a20140919d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGraphs and Matrices /$fby Ravindra B. Bapat 205 $a2nd ed. 2014. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2014. 215 $a1 online resource (XI, 193 p. 32 illus.)$conline resource 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4471-6568-3 327 $aPreliminaries -- 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. 330 $aThis new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering. 410 0$aUniversitext,$x0172-5939 606 $aMatrix theory 606 $aAlgebra 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 615 0$aMatrix theory. 615 0$aAlgebra. 615 14$aLinear and Multilinear Algebras, Matrix Theory. 676 $a512.5 700 $aBapat$b Ravindra B$4aut$4http://id.loc.gov/vocabulary/relators/aut$0147505 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299983303321 996 $aGraphs and matrices$9766815 997 $aUNINA 999 $aThis 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