#### 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.

Done