Time: 6.4.2021 at 13:00
Speaker: Anni Hakanen, University of Turku
Title: On the Forced Vertices of Resolving Sets and Metric Bases of Graphs
Abstract: A resolving set of a graph is a subset of the vertices which gives a unique combination of distances to each vertex of the graph. Resolving sets can be used to locate vertices in a graph. A resolving set of minimum cardinality is called a metric basis of the graph. In this talk, we will discuss how the concept of a resolving set can be generalised to locate vertex sets instead of individual vertices. Special emphasis is placed on characterising vertices that are necessary to locate vertex sets. A vertex that is in all such resolving sets is called a forced vertex. Forced vertices do not exist for resolving sets that can locate one vertex at a time. However, we can define a similar concept for the metric bases of graphs.