Partial sum of eigenvalues of random graphs

0524781 - ÚI 2021 RIV CZ eng J - Journal Article
Rocha, Israel
Partial sum of eigenvalues of random graphs.
Applications of Mathematics. Roč. 65, č. 5 (2020), s. 609-618. ISSN 0862-7940. E-ISSN 1572-9109.
[MAT TRIAD 2019. International Conference on Matrix Analysis and its Applications /8./. Liblice, 08.09.2019-13.09.2019]
R&D Projects: GA ČR(CZ) GA19-08740S
Institutional support: RVO:67985807
Keywords : sum of eigenvalues * graph energy * random matrix
OECD category: Pure mathematics
Impact factor: 0.881, year: 2020
Method of publishing: Open access with time embargo

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.
Permanent Link: http://hdl.handle.net/11104/0309071