Strong and Weak 2-Vertex Duplication Self Switching of a Disconnected Graphs

Abstract

: A vertex  in  is said to be a duplication of  in  if all the vertices which are adjacent to  are also adjacent to  vertex duplication of a graph  is the duplication of any two vertices  is  such that  are adjacent to all the vertices that are adjacent to The vertex duplication switching of G by is the graph obtained by duplicating any two vertices  then by removing all existing edges between  and its complement  in  and also by adding  edges between  and   which are not in G, without affecting the adjacency and non-adjacency of vertices in