The Energy of Graphs and Matrices Laura Buggy, College of St. Benedict Amalia Culiuc, Mount Holyoke College Katelyn Mccall, University of Rochester

Let G be a finite, undirected, and simple graph. If {v1, · · · , vn} is the set of vertices of G, then the adjacency matrix A(G) = [aij ] is an n-by-n matrix where aij = 1 if vi and vj are adjacent and aij = 0 otherwise. The energy of a graph, E(G), is defined as the sum of the absolute values of eigenvalues of A(G). The concept of energy originates in chemistry and was first defined by I. Gutman in 1978. It has been generalized recently as follows: For a graph G on n vertices, let M be a matrix associated with G. Let μ1, · · · , μn be the eigenvalues of M and let μ̄ be the average of μ1, · · · , μn. The more general M -energy of G is then defined as: EM (G) = n ∑