3 papers
cs.CC2025
On a Hierarchy of Spectral Invariants for Graphs
V. Arvind, Frank Fuhlbrück, Johannes Köbler +1
We consider a hierarchy of graph invariants that naturally extends the spectral invariants defined by Fürer (Lin. Alg. Appl. 2010) based on the angles formed by the set of standar…
cs.DM2024
Gathering Information about a Graph by Counting Walks from a Single Vertex
Frank Fuhlbrück, Johannes Köbler, Oleg Verbitsky +1
We say that a vertex in a connected graph is decisive if the numbers of walks from of each length determine the graph rooted at up to isomorphism among all conn…
cs.CC2024
On the Expressibility of the Reconstructional Color Refinement
V. Arvind, Johannes Köbler, Oleg Verbitsky
One of the most basic facts related to the famous Ulam reconstruction conjecture is that the connectedness of a graph can be determined by the deck of its vertex-deleted subgraphs,…