Soft Graphs of Certain Graphs

Let G^∗ = (V, E) be a simple graph and A be any nonempty set of parameters. Let subset R of A×V be an arbitrary relation from A to V. A mapping from A to ᵖ(V) written as F:A → ᵖ(V) can be defined as F(x) = { y ∈ V/xRy} and a mapping from A to ᵖ(E) written as K:A → ᵖ(E) can be defined as K(x) = {uv ∈ E/{u, v} ⊆ F(x)}. The pair (F, A) is a soft set over V and the pair (K, A) is a soft set over E. Obviously (F(a), K(a)) is a subgraph of G^∗ for all a ∈ A. The 4-tuple G = ( G^∗, F, K, A) is called a soft graph of G. In this paper we discuss different soft graphs of graphs such as Complete graph, Star graph, Complete bipartite graph, Crown graph, Comb graph, Friendship graph, Bistar graph and Wheel graph.