Descripción del título
An Introduction to the Theo...
A self-contained introduction to the theory of graph spectra including exercises and an extensive bibliography
Monografía
monografia Rebiun39060181 https://catalogo.rebiun.org/rebiun/record/Rebiun39060181 m o d cr ||||||||||| 101021s2009 enk ob 001 0 eng d 797859066 831670032 976523669 1167531487 1481192271 9780511801518 ebook) 0511801513 ebook) 9780521118392 hardback) 0521118395 hardback) 9781107365704 1107365708 9781107360792 electronic bk.) 110736079X electronic bk.) 0521134080 9780521134088 9781139244596 1139244590 AU@ 000055792486 DEBSZ 381830160 DEBSZ 445574054 UkCbUP eng pn AUD OCLCO CUY OCLCQ OCLCO MHW EBLCP OCLCF DEBSZ OCLCQ N$T E7B YDXCP IDEBK OCLCQ AU@ OCLCQ UKAHL OCLCO OCLCQ OCLCO OCLCL OCLCQ UKKRT OCLCQ OCLCL MAT 013000 bisacsh 511.5 https://id.oclc.org/worldcat/ddc/E38QCPfWTdh6pf4kgCFdtTHHrm An Introduction to the Theory of Graph Spectra Dragos Cvetkovic, Peter Rowlinson, Slobodan Simic Cambridge Cambridge University Press 2009 Cambridge Cambridge Cambridge University Press 1 online resource (378 pages) 1 online resource (378 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society Student Texts no. 75 Title from publishers bibliographic system (viewed 22 Dec 2011) Includes bibliographical references (pages 333-357) and indexes Cover; Title; Copyright; Contents; Preface; 1 Introduction; 1.1 Graph spectra; 1.2 Some more graph-theoretic notions; 1.3 Some results from linear algebra; Exercises; Notes; 2 Graph operations and modifications; 2.1 Complement, union and join of graphs; 2.2 Coalescence and related graph compositions; 2.3 General reduction procedures; 2.4 Line graphs and related operations; 2.5 Cartesian type operations; 2.6 Spectra of graphs of particular types; Exercises; Notes; 3 Spectrum and structure; 3.1 Counting certain subgraphs; 3.2 Regularity and bipartiteness; 3.3 Connectedness and metric invariants 3.4 Line graphs and related graphs3.5 More on regular graphs; 3.5.1 The second largest eigenvalue; 3.5.2 The eigenvalue with second largest modulus; 3.5.3 Miscellaneous results; 3.6 Strongly regular graphs; 3.7 Distance-regular graphs; 3.8 Automorphisms and eigenspaces; 3.9 Equitable partitions, divisors and main eigenvalues; 3.10 Spectral bounds for graph invariants; 3.11 Constraints on individual eigenvalues; 3.11.1 The largest eigenvalue; 3.11.2 The second largest eigenvalue; Exercises; Notes; 4 Characterizations by spectra; 4.1 Spectral characterizations of certain classes of graphs 4.1.1 Elementary spectral characterizations4.1.2 Graphs with least eigenvalue -2; 4.1.3 Characterizations according to type; 4.2 Cospectral graphs and the graph isomorphism problem; 4.2.1 Examples of cospectral graphs; 4.2.2 Constructions of cospectral graphs; 4.2.3 Statistics of cospectral graphs; 4.2.4 A comparison of various graph invariants; 4.3 Characterizations by eigenvalues and angles; 4.3.1 Cospectral graphs with the same angles; 4.3.2 Constructing trees; 4.3.3 Some characterization theorems; Exercises; Notes; 5 Structure and one eigenvalue; 5.1 Star complements 7.5.3 Isoperimetric problems7.6 Expansion; 7.7 The normalized Laplacian matrix; 7.8 The signless Laplacian; 7.8.1 Basic properties of Q-spectra; 7.8.2 Q-eigenvalues and graph structure; 7.8.3 The largest Q-eigenvalue; Exercises; Notes; 8 Some additional results; 8.1 More on graph eigenvalues; 8.1.1 Graph perturbations; 8.1.2 Bounds on the index; 8.2 Eigenvectors and structure; 8.3 Reconstructing the characteristic polynomial; 8.4 Integral graphs; Exercises; Notes; 9 Applications; 9.1 Physics; 9.1.1 Vibration of a membrane; 9.1.2 The dimer problem; 9.2 Chemistry A self-contained introduction to the theory of graph spectra including exercises and an extensive bibliography Graph theory Matrices Matrices MATHEMATICS- Graphic Methods. Graph theory. Matrices. Cvetkovic, Dragos Rowlinson, Peter Simic, S. Slobodan) Print version 9780521118392 London Mathematical Society student texts no. 75