Consider the spanning trees T 1 and T 2 in the proof of Theorem 10.6.3. Prove that w ( T 2 ) ≤ w ( T 1 ) .

To prove:

w(T2)≤w(T1),

Where, T2 is the graph obtained from T1 by removing e' and adding e, whereas w(e')≥w(e).

Given information:

Spanning trees are T1 and T2.

Concept used:

Correctness of Prim’s Algorithm:

When a connected, weighted graph G is input to prim’s algorithm, the output is a minimal spanning tree for G.

Calculation:

In the proof of given theorem, the following are the facts:

T2 is the graph obtained from T1 by removing e' and adding e.

Also w(e')≥w(e)