Cosplitting and co – regular graphs

The graph S(G) obtained from a graph G(V,E), by adding a new vertex w for every vertex v  V and joining w to all neighbours of v in G, is called the splitting graph of G. The cosplitting graph CS(G) is obtained from G, by adding a new vertex w for each vertex v  V and joining w to those vertices of G which are not adjacent to v in G. In this paper, we introduce the concept of cosplitting graph and characterise the graphs for which splitting and cosplitting graphs are isomorphic.