Alladi Ramakrishnan Hall

Critical groups of graphs

Pantangi Venkata Raghu Tej

University of Florida

The critical group of a graph is an interesting isomorphic invariant. It is a finite abelian group whose order is equal
to the number of spanning forests in the graph. The Smith normal form of the graph's Laplacian determines the
structure of its critical group. In this presentation, we will consider a family of strongly regular graphs. We will apply
representation theory of groups of automorphisms to determine the critical groups of graphs in this family.