  Recent work shows that a new family of norms on Hermitian matrices arise by
evaluating the even degree complete homogeneous symmetric (CHS) polynomials on
the eigenvalues of a Hermitian matrix. The CHS norm of a graph is then defined
by evaluating the even degree CHS polynomials on the eigenvalues of the
adjacency matrix of a graph. The fact that these norms are defined in terms of
eigenvalues (as opposed to singular values) ensures they can distinguish
between graphs that other norms cannot. In addition, we prove that the CHS
norms are minimized over all connected graphs by the path and maximized over
all connected graphs by the complete graph. Finally, we prove that the CHS
norms are minimized over all trees by the path and maximized over all trees by
the star. Our paper is intended for a wide mathematical audience and we assume
no prior knowledge about graphs or symmetric polynomials.
