Partial sum of eigenvalues of random graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F20%3A00524781" target="_blank" >RIV/67985807:_____/20:00524781 - isvavai.cz</a>
Result on the web
<a href="http://hdl.handle.net/11104/0309071" target="_blank" >http://hdl.handle.net/11104/0309071</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2020.0352-19" target="_blank" >10.21136/AM.2020.0352-19</a>

Result language
angličtina
Original language name
Partial sum of eigenvalues of random graphs
Original language description
Let G be a graph on n vertices and let lambda(1) >= lambda(2) >= ... >= lambda(n) be the eigenvalues of its adjacency matrix. For random graphs we investigate the sum of eigenvalues s(k)= Sigma(k)(i=1)lambda(i) for 1 <= k <= n, and show that a typical graph has S-k <= (e(G) +k(2))/(0.99n)(1/2), where e(G) is the number of edges of G. We also show bounds for the sum of eigenvalues within a given range in terms of the number of edges. The approach for the proofs was first used in Rocha (2020) to bound the partial sum of eigenvalues of the Laplacian matrix.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA19-08740S" target="_blank" >GA19-08740S: Embedding, Packing and Limits in Graphs</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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