Title: Symmetric and Skew-Symmetric Signing for Graphs
| Speaker: | Sho Suda |
| Affiliation: |
National Defense Academy of Japan |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract:
We consider symmetric and skew-symmetric signings for graphs. A signing for a graph G = (V, E) is a mapping σ : (x, y) | x, y in V \} to {0, ± 1} with the following properties:
- σ(x, y) ≠ 0 if and only if {x, y} in E,
- σ(x, y) = σ(y, x) for any distinct x, y in V with {x, y} in E.
For a signing σ of a graph, we define the signed adjacency matrix A_σ of the graph, where the (x, y)-entry of A_σ is equal to σ(x, y). We study the problem of finding lower bounds for the spectral radius of A_σ and aim to determine a signing for a given graph such that its spectral radius is the smallest among all possible signings of that graph. A signing of a small spectral radius plays an important role in constructing Ramanujan graphs. Additionally, we consider a variation of signing, which we call skew-symmetric signing for graphs.
This talk is based on joint work with Jack Koolen and Hadi Kharaghani.