Number of Components in the Graph Exponential with Complete Graph Exponents

Although Lov\'{a}sz introduced the graph exponential GK in 1967, this product has received little attention. This paper focuses on the number of components in GK when exponent K is a complete graph Kₙ. For a connected bipartite G, when K is K₂, GK₂ has three components; and when K is Kₙ with $n>2$, GKₙ produces +1/2 components. A connected G with an odd cycle produces one component in GKₙ.