Algebraic Graph Theory Seminar - Cristina DalfóExport this event to calendar

Monday, December 6, 2021 — 11:30 AM EST

Title: On the Laplacian spectra of token graphs

Speaker: Cristina Dalfó
Affiliation: Universitat de Lleida
Zoom: Contact Soffia Arnadottir

Abstract:

We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph F_k(G)of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this talk, we give a relationship between the Laplacian spectra of any two token graphs of a given graph. In particular, we show that, for any integers such that 1 ≤h ≤k≤n2, the Laplacian spectrum of Fh(G)is contained in the Laplacian spectrum of Fk(G). Besides, we obtain a relationship between the spectra of the k-token graph of G and the k-token graph of its complement. This generalizes to tokens graphs a well-known property stating that the Laplacian eigenvalues of G are closely related to the Laplacian eigenvalues of the complement of G. Finally, we conjecture that the algebraic connectivities of the original graph and its k-token graph coincide.

Event tags 

S M T W T F S
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1
2
3
4
  1. 2022 (69)
    1. June (1)
    2. May (16)
    3. April (12)
    4. March (18)
    5. February (10)
    6. January (13)
  2. 2021 (103)
    1. December (3)
    2. November (7)
    3. October (6)
    4. September (12)
    5. August (6)
    6. July (10)
    7. June (12)
    8. May (7)
    9. April (9)
    10. March (13)
    11. February (8)
    12. January (10)
  3. 2020 (119)
  4. 2019 (167)
  5. 2018 (136)
  6. 2017 (103)
  7. 2016 (137)
  8. 2015 (136)
  9. 2014 (88)
  10. 2013 (48)
  11. 2012 (39)
  12. 2011 (36)
  13. 2010 (40)
  14. 2009 (40)
  15. 2008 (39)
  16. 2007 (15)