Graph Contraction and Connectivity Parallel and Sequential Data

Definition 1.3 (Subgraph). Let G = (V, E) and H = (V ′, E′) be two graphs. H is a subgraph of G if V ′ ⊆ V and E′ ⊆ E. H is a proper subgraph is V ′ ( V or E′ ( E. Definition 1.4 (Vertex Induced Subgraph). Let G = (V, E) and V ′ ⊆ V . The subgraph of G induced by V is a graph H = (V ′, E′) where E′ = {{u, v} ∈ E|u ∈ V ′, v ∈ V ′}. Definition 1.5 (Edge Induced Subgraph). Let G = (V, E) and E′ ⊆ E. The subgraph of G induced by E is a graph H = (V ′, E′) where V ′ = {u|u ∈ {v, w} ∈ E′}.