About Adjacency Matrix of Semigraphs

—The aim of the paper is to define the adjacency matrix of a Semigraph. We expect to see many applications of this in the future. Incidence matrix of a semigraph has been defined by the authors[4].Here we not only define Adjacency Matrix associated with a semigraph, but also state necessary and sufficient conditions for a matrix to be semigraphical. At the end of the paper spectrum of a semigraph is defined and some of its spectral properties are studied. Index Terms—Adjacency matrix of a semigraph, spectrum of a semigraph.