AbstractExtremal eigenvalues of graphs are of particular interest in theoretical computer science and combinatorics. Specifically, the spectral gap—the gap between the first and second largest eigenvalues—measures the expanding property of the graph. In this talk, I will focus on random $d$-regular graphs, for which the largest eigenvalue is $d$.I'll first explain some conjectures on the extr...
IntroductionCurrently the problem of transferring results of algebraic topology to discrete objects and, in particular, to various categories of digraphs and graphs, is widely investigated. The main technical tools are given by the homotopy theory and various homology theories. We present the basic methods of algebraic topology in graph theory and describe relations between continious and discr...
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