Problem

Prove parts (a) and (b) of Theorem 3.5.4. Keep in mind that C (v) and C (w) are graphs;...

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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Solutions For Problems in Chapter 3.5