This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.

Spectra of graphs

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Methods Of Modern Mathematical Physics

Probability and Measure

Distance-Regular Graphs

Combinatorial Group Theory: COMBINATORIAL GROUP THEORY

White Noise Calculus and Fock Space

Quantum Probability and Orthogonal Polynomials- Adjacency Matrices- Distance-Regular Graphs- Homogeneous Trees- Hamming Graphs- Johnson Graphs- Regular Graphs- Comb Graphs and Star Graphs- The Symmetric Group and Young Diagrams- The Limit Shape of Young Diagrams- Central Limit Theorem for the Plancherel Measures of the Symmetric Groups- Deformation of Kerov's Central Limit Theorem

Quantum Probability and Spectral Analysis of Graphs

/pdf/an-analytic-characterization-of-symbols-of-operators-on-6i7w98xcfv.pdf

An analytic characterization of symbols of operators on white noise functionals

The theory of generalized white noise functionals (white noise calculus) initiated in [2] has been considerably developed in recent years, in particular, toward applications to quantum physics, see e.g. [5], [7] and references cited therein. On the other hand, since H. Yoshizawa [4], [23] discussed an infinite dimensional rotation group to broaden the scope of an investigation of Brownian motion, there have been some attempts to introduce an idea of group theory into the white noise calculus. For example, conformal invariance of Brownian motion with multidimensional parameter space [6], variational calculus of white noise functionals [14], characterization of the Levy Laplacian [17] and so on.

/pdf/infinite-dimensional-rotations-and-laplacians-in-terms-of-4wowv6fp6b.pdf

Nobuaki Obata

Papers

Distance-Regular Graphs

White Noise Calculus and Fock Space

Quantum Probability and Spectral Analysis of Graphs

An analytic characterization of symbols of operators on white noise functionals

Infinite-dimensional rotations and Laplacians in terms of white noise calculus