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 $...

Because of the presence of Jacobian terms, determinants which arose as a result of a transformation of variables, many common likelihood functions have singularities. This fact has several implications for maximum likelihood estimation. The most interesting of these is that singularities often correspond with economically meaningful restrictions, and they can be used to impose the latter. Sever...

We prove that the maximum determinant of an n×n matrix, with entries in {0,1} and at most n+k non-zero entries, is 2k/3, which best possible when k a multiple 3. This result solves conjecture Bruhn Rautenbach. also obtain upper bound on number perfect matchings C4-free bipartite graphs based edges, which, sparse case, improves classical Bregman's inequality for permanents. tight, as equality ac...