Which graphs are determined by their spectrum

By E. V. Dam, Willem H. Haemers. 2003

780 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2ee19196a8680f80a37816710d6c514c06ea8901

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Signless Laplacians and line graphs (2005, methodology): “In this paper we study the phenomenon of cospectrality in graphs by comparing characterizing properties of spectra of graphs and spectra of their line graphs.”
On the second largest Laplacian eigenvalues of graphs (2005, background): “Moreover, it is well known that the number of edges(or vertices) of a graph can be determined by its L-spectrum, see [5].”
Spectra of Graphs (2011, methodology): “51 3.7.2 The Haemers bound on the Shannon capacity . . . . . .”
On the A-characteristic polynomial of a graph (2017, background): “Up until now, although many graphs have been proved to be DS graphs (see [4, 5]), the problem of determining DS graphs is still far from being completely solved.”
EIGENVALUE BOUNDS FOR THE SIGNLESS LAPLACIAN (2007, background): “Regular graphs can be recognized, and the degree of regularity and the number of components calculated, from QG(λ), as noticed in [10].”
Starlike trees are determined by their Laplacian spectrum (2007, background): “For the background and some known results about this problem, we refer the reader to [9] and the references therein.”
Unoriented Laplacian maximizing graphs are degree maximal (2008, background): “Some people have expressed the view that, in comparison to the spectra of other commonly used graph matrices (such as the Laplacian and the adjacency matrix), the signless Laplacian seems to be the most convenient for use in studying graph properties (see [11]).”
Spectral characterizations of lollipop graphs (2008, neutral): “(In [2], the operation is called Godsil-McKay switching.”
A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas (2018, background): “Follows up Lee, Lucchese, and Chu (1987a) and Lee and Gutman (1989a), calculating net signs of eigenspatially signed hypercube graphs of dimensions up to 6 by means of a general graph-product formula.”
Signless Laplacians of finite graphs (2007, methodology): “The papers [8,15] provide spectral uncertainties rn with respect to the adjacency matrix and qn with respect to the signless Laplacian of sets of all graphs on n vertices for n 11:”
Graphs with integral spectrum (2009, neutral): “Thus, using Lemmas 9 and 8 we see that there are at most∑ −7 √ n≤λ≤7 √ n ∑ t≤s≤n−|λ| Nλ(n, s) ≤ (14 √ n+ 1) ( n t ) 2n(n−1)/2−t(t−1)/2+1 matrices in this set having an integral spectrum.”
Some properties of the distance Laplacian eigenvalues of a graph (2013, background): “It is known [26] that the adjacency and (adjacency) Laplacian spectra are equivalent over the class of degree regular graphs.”
Merging the A- and Q-spectral theories (2016, background): “It is worth pointing out that the family Aα (G) is just a small subset of the generalized adjacency matrices defined in [10] and the universal adjacency matrices defined in [16].”