Prove parts (a) and (b) of Theorem 3.5.4. Keep in mind that C (v) and C (w) are graphs; to be the same they must have the same vertices and the same edges.
Reference:
Theorem 3.5.4
For each vertex v in a graph G, let be the component of v in G. Then
(a) C (v) = C (w) iff w is reachable from v.
(b) C (v) ≠C (w) iff no vertex is in both C (v) and C (w).
(c) for each v, C (v) is connected.
(d) for each v, C (v) is a maximally connected subgraph of G.
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