Algebraic Graph Theory International Webinar (27.12.2022)

v utorok 27.12.2022 o 19:00 hod.

26. 12. 2022 18.34 hod.
Od: Róbert Jajcay

The organizers of the Algebraic Graph Theory International Webinar would like to invite you to join us and other colleagues on December 27, 2022, at 7pm Central European Summer Time (= 6pm UTC), for the next presentation delivered by Cristina Dalfo.

The title of Cristina's talk: The algebraic connectivity of token graphs

Abstract:
We study the algebraic connectivity (or second Laplacian eigenvalue) of tokengraphs, 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 are adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. Recently, it was conjectured that the algebraic connectivity of $F_k(G)$ equals the algebraic connectivity of G. In this talk, we prove the conjecture for new infinite families of graphs, such as trees, some graphs with hanging trees, graphs with minimum degree large enough. In these families are included the following graphs: the cocktail party graph, the complement graph of a cycle, the complete multipartite graph, etc. We also show the conjecture for cycles $C_n$ when $k=2$ for most cases of $n$.

The Zoom link for this semester is:
https://uni-lj-si.zoom.us/j/92545586220?pwd=Vjc4cytxaVBFbFJXY0Q4L2RhOUZHZz09
Meeting ID: 925 4558 6220
Passcode: 117532

Further details may be found at http://euler.doa.fmph.uniba.sk/AGTIW.html

where you can also find the slides and the recordings of our previous presentations. Also, if you wish to advertise an AGT friendly conference on this page, please send us the link.

Hoping to see you at the webinar, and wishing you all the best.

Isabel Hubard, Robert Jajcay and Primoz Potocnik