Geodesic
An interlacing property of the signless Laplacian of threshold graphs
Christoph Helmberg1 ; Guilherme Porto2 ; Guilherme Torres3 ; Vilmar Trevisan4
1TU Chemnitz, Fakultät für Mathematik
2Instituto Federal de Educação, Ciência e Tecnologia Farroupilha, Campus São Borja
3deceased, before: Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Porto Alegre
4Instituto de Matemática, Universidade Federal do Rio Grande do Sul
The electronic journal of combinatorics, Tome 32 (2025) no. 1
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We show that for threshold graphs, the eigenvalues of the signless Laplacian matrix interlace with the degrees of the vertices. As an application, we show that the signless Brouwer conjecture holds for threshold graphs, i.e., for threshold graphs the sum of the $k$ largest eigenvalues is bounded by the number of edges plus $k + 1$ choose $2$.
DOI : 10.37236/12332
Classification : 05C50, 15A18
Mots-clés : signless Laplacian matrix, signless Brouwer conjecture

Christoph Helmberg  1   ; Guilherme Porto  2   ; Guilherme Torres  3   ; Vilmar Trevisan  4

1 TU Chemnitz, Fakultät für Mathematik
2 Instituto Federal de Educação, Ciência e Tecnologia Farroupilha, Campus São Borja
3 deceased, before: Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Porto Alegre
4 Instituto de Matemática, Universidade Federal do Rio Grande do Sul 
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     title = {An interlacing property of the signless {Laplacian} of threshold graphs},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
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     doi = {10.37236/12332},
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Christoph Helmberg; Guilherme Porto; Guilherme  Torres; Vilmar Trevisan. An interlacing property of the signless Laplacian of threshold graphs. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/12332

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