The γ-graph of a graph For a graph G = (V, E), the γ-graph of G, G(γ) = (V (γ), E(γ)), is the reconfiguration graph whose vertex set is the collection of minimum dominating sets, or γ-sets of G, and two γ-sets are adjacent in G(γ) if they differ by a single vertex and the two different vertices are adjacent in G. The γ-graph of G was introduced by Fricke et al. in 2011 where they studied properties of γ-graphs,…

Dynamical algebraic combinatorics and independence sets of graphs Dynamical algebraic combinatorics is a relatively new (and fun!) topic, which looks at cyclic group actions on objects from algebraic combinatorics, inspired by some questions coming from dynamical systems. I will give an introduction to the area, focusing on an action I have defined with Nathan Williams on the independent sets of a graph (arXiv:1805.00815). We also construct a partial order on the set of independent sets of a graph, which may…

The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).

The localization game played on graph Graph searching investigates combinatorial models for the detection or neutralization of an adversary’s activity on a network. One such model is the localization game, where pursuers use distance probes to capture an invisible evader. We present new results on the localization number of a graph, which is the minimum number of pursuers needed to capture the evader. We survey what is known and unknown for the localization number, discuss connections with the chromatic number,…