000 04712cam a2200445Mi 4500
001 ocn896835905
003 OCoLC
005 20190328114809.0
006 m o d
007 cr cn|||||||||
008 141021t20152015enka ob 001 0 eng d
040 _aE7B
_beng
_erda
_epn
_cE7B
_dUIU
_dOCLCF
_dOPELS
_dCOO
_dOCLCQ
_dFEM
_dOCLCQ
_dU3W
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019 _a968008290
_a969073233
020 _a9780128020975
_q(e-book)
020 _a0128020970
_q(e-book)
020 _a0128020687
020 _a9780128020685
020 _z9780128020685
035 _a(OCoLC)896835905
_z(OCoLC)968008290
_z(OCoLC)969073233
050 4 _aQA166
_b.S74 2015eb
082 0 4 _a511/.5
_223
100 1 _aStevanovi�c, Dragan,
_eauthor.
245 1 0 _aSpectral radius of graphs /
_h[electronic resource]
_cDragan Stevanovi�c.
264 1 _aLondon :
_bElsevier,
_c2015
264 4 _c�2015
300 _a1 online resource (167 pages) :
_billustrations
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_2rda
504 _aIncludes bibliographical references and index.
588 0 _aOnline resource; title from PDF title page (ebrary, viewed October 21, 2014).
520 _aSpectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the book delves deeper into the properties of the principal eigenvector; a critical subject as many of the results on the spectral radius of graphs rely on the properties of the principal eigenvector for their proofs. A following chapter surveys spectral radius of special graphs, covering multipartite graphs, non-regular graphs, planar graphs, threshold graphs, and others. Finally, the work explores results on the structure of graphs having extreme spectral radius in classes of graphs defined by fixing the value of a particular, integer-valued graph invariant, such as: the diameter, the radius, the domination number, the matching number, the clique number, the independence number, the chromatic number or the sequence of vertex degrees. Throughout, the text includes the valuable addition of proofs to accompany the majority of presented results. This enables the reader to learn tricks of the trade and easily see if some of the techniques apply to a current research problem, without having to spend time on searching for the original articles. The book also contains a handful of open problems on the topic that might provide initiative for the reader's research. Dedicated coverage to one of the most prominent graph eigenvalues Proofs and open problems included for further study Overview of classical topics such as spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem.
505 0 _aFront Cover; Spectral Radius of Graphs; Copyright; Dedication; Contents; Preface; Chapter 1: Introduction; 1.1 Graphs and Their Invariants; 1.2 Adjacency Matrix, Its Eigenvalues, and Its Characteristic Polynomial; 1.3 Some Useful Tools from Matrix Theory; Chapter 2: Properties of the Principal Eigenvector; 2.1 Proportionality Lemma and the Rooted Product; 2.2 Principal Eigenvector Components Along a Path; 2.3 Extremal Components of the Principal Eigenvector; 2.4 Optimally Decreasing Spectral Radius by Deleting Vertices or Edges; 2.4.1 Vertex Removal; 2.4.2 Edge Removal.
505 8 _a2.5 Regular, Harmonic, and Semiharmonic GraphsChapter 3: Spectral Radius of Particular Types of Graphs; 3.1 Nonregular Graphs; 3.2 Graphs with a Given Degree Sequence; 3.3 Graphs with a Few Edges; 3.3.1 Trees; 3.3.2 Planar Graphs; 3.4 Complete Multipartite Graphs; Chapter 4: Spectral Radius and Other Graph Invariants; 4.1 Selected AutoGraphiX Conjectures; 4.2 Clique Number; 4.3 Chromatic Number; 4.4 Independence Number; 4.5 Matching Number; 4.6 The Diameter; 4.7 The Radius; 4.8 The Domination Number; 4.9 Nordhaus-Gaddum Inequality for the Spectral Radius; Bibliography; Index.
650 0 _aGraph theory.
650 7 _aGraph theory.
_2fast
_0(OCoLC)fst00946584
655 4 _aElectronic books.
856 4 0 _3ScienceDirect
_uhttp://www.sciencedirect.com/science/book/9780128020685
999 _c247004
_d247004