Encryption System Involving Matrix Associated With Semigraphs

Semigraphs are a generalization of graphs, where an edge is allowed to have two or more vertices. A binomial incidence matrix is an incidence matrix of a semigraph which represents the semigraph uniquely. We prove that, the binomial incidence matrix of any semigraph belonging to one of two specific classes of semigraphs, is invertible. Then we note a peculiar property enjoyed by the columns of a submatrix of the adjoint of the binomial incidence matrix of semigraphs under consideration. By making use of this property, we develop an encryption system which uses invertibility of the binomial incidence matrix.