Topics in Spectral Graph Theory - Tapa blanda

Sinopsis

Algebraic graph theory is the branch of mathematics that studies graphs by using algebraic properties of associated matrices. Spectral graph theory studies the relation between graph properties and the spectrum of the adjacency or Laplacian matrix.Google founders computed the Perron-Frobenius eigenvector of the web graph and became billionaires. The second largest eigenvalue of a graph gives information about expansion and randomness properties with smallest eigenvalue gives information about independence and chromatic number. Interlacing gives information about substructures. Eigenvalue multiplicities provides strong restrictions with the spectrum providing useful invariants.The standard material on spectra is first provided. Important applications of graph spectra involve the largest or second largest or smallest eigenvalue, or interlacing, topics are then presented. Special topics of trees, topological structures and spectral characterizations are discussed.

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