Addition Operation In Semigraphs^∗

The addition of graphs is a well-studied operation on graphs which results in a new graph with more number of vertices and edges. The operation of adding vertices to graphs is different from the addition of graphs but also defines a new graph with more number of vertices and edges. In this article, the above two operations are extended to a generalization of graphs called semigraphs. The article also deals with the rank of a special incidence matrix of semigraphs resulting by the application of the above two operations.