determinants of adjacency matrices of graphs

we study the set of all determinants of adjacency matrices of graphs with a given number of vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. using an idea of m. newman, it is proved that if $g$ is a graph with $n$ vertices and ${d_1,dots,d_n}$ is the set of vertex degrees of $g$, then $gcd(2m,d^2)$ divides the determinant of the adjacency matrix of $g$, where $d=gcd(d_1,dots,d_n)$. possible determinants of adjacency matrices of graphs with exactly two cycles are obtained.