DETERMINANTS OF ADJACENCY MATRICES OF GRAPHS

We study the set of all determinants of adjacency matrices of graphs with a given numberof vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most9 vertices are computed so that the number of non-isomorphic graphs with given vertices whose deter-minants are all equal to a number is exhibited in a table. using an idea of m. newman, it is provedthat if g is a graph with n vertices, m edges and fd1; : : : ; dng is the set of vertex degrees of g, thengcd(2m; d2) divides the determinant of the adjacency matrix of g, where d = gcd(d1; : : : ; dn). possibledeterminants of adjacency matrices of graphs with exactly two cycles are obtained.