Recovering quantum graphs from their Bloch spectrum

Recovering Fields from Their Decomposition Graphs

Recall that the birational anabelian conjecture originating in ideas presented in Grothendieck’s Esquisse d’un Programme [G1] and Letter to Faltings [G2], asserts roughly the following: First, there should exist a group theoretical recipe by which one can recognize the absolute Galois groups GK of finitely generated infinite fields K among all the profinite groups. Second, if G = GK is such an ...

The spectrum of the hyper-star graphs and their line graphs

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...

Which graphs are determined by their spectrum?

For almost all graphs the answer to the question in the title is still unknown. Here we survey the cases for which the answer is known. Not only the adjacency matrix, but also other types of matrices, such as the Laplacian matrix, are considered. © 2003 Elsevier Inc. All rights reserved.

Reconstruction of Weighted Graphs by their Spectrum

Recovering Plane Curves from Their Bitangents

1.1. It is well known that a general plane curve of degree d has 12d(d − 2)(d − 9) distinct bitangent lines. The first (and most) interesting case is that of a smooth plane quartic X , whose configuration of 28 bitangents we shall denote by θ(X), to highlight the correspondence with the odd theta-characteristics of X . The properties of θ(X) have been extensively studied by the classical geomet...