k-vertex Self Switching of Complete Bipartite Graph

Abstract

For a finite undirected graph G(V, E) and a non-empty set σ ⊆ V , the switching of G by σ is defined
as the graph G
σ
(V, E0
) which is obtained from G by removing all edges between σ and its complement
V −σ and adding as edges all non-edges between σ and V −σ. If G ∼= G
σ
, then σ is called as self switching of G and if | σ |= k, then it is called as k-vertex self switching. The set of all k-vertex self switchings of G is denoted by SSk(G) and its cardinality by ssk(G). In this paper, we give a sufficient condition for σ
to be a k-vertex self switching for a complete bipartite graph and we find ssk(G) of complete bipartite graph.