02380nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100002700213245008800240260008200328300003400410336002600444337002600470338003600496347002400532490003900556506006600595520111900661650004101780650002301821650002301844650005501867856003201922856006401954233-180518CH-001817-320180518233001.0a fot ||| 0|cr nn mmmmamaa180518e20180530sz fot ||| 0|eng d a978303719688570a10.4171/1882doi ach0018173 7aPBV2bicssc a05-xxa11-xxa15-xx2msc1 aNica, Bogdan,eauthor.10aA Brief Introduction to Spectral Graph Theoryh[electronic resource] /cBogdan Nica3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (168 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aSpectral graph theory starts by associating matrices to graphs – notably, the adjacency matrix and the Laplacian matrix. The general theme is then, firstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenvalues to structural properties of graphs. As it turns out, the spectral perspective is a powerful tool. Some of its loveliest applications concern facts that are, in principle, purely graph theoretic or combinatorial. This text is an introduction to spectral graph theory, but it could also be seen as an invitation to algebraic graph theory. The first half is devoted to graphs, finite fields, and how they come together. This part provides an appealing motivation and context of the second, spectral, half. The text is enriched by many exercises and their solutions. The target audience are students from the upper undergraduate level onwards. We assume only a familiarity with linear algebra and basic group theory. Graph theory, finite fields, and character theory for abelian groups receive a concise overview and render the text essentially self-contained.07aCombinatorics & graph theory2bicssc07aCombinatorics2msc07aNumber theory2msc07aLinear and multilinear algebra; matrix theory2msc40uhttps://doi.org/10.4171/188423cover imageuhttps://www.ems-ph.org/img/books/nica_mini.jpg