GATE2009-38

Question

Consider the following graph:

          

Which one of the following is NOT the sequence of edges added to the minimum spanning tree using Kruskal’s algorithm?

• A. $\text{(b, e) (e, f) (a, c) (b, c) (f, g) (c, d)}$

• B. $\text{(b, e) (e, f) (a, c) (f, g) (b, c) (c, d)}$

• C. $\text{(b, e) (a, c) (e, f) (b, c) (f, g) (c, d)}$

• D. $\text{(b, e) (e, f) (b, c) (a, c) (f, g) (c, d)}$

Comments

$Remark:$
In Kruskal's algorithm, Edges are sorted in ascending order in O(ElogE) time. Any edge with larger weight can't be added before an edge with the smaller weight.
(D) is the correct choice, b-c can't added before a-c.

---

@Manu Thakur Sir pls help.. i dont understand y m i stuck with the answer of this simple problem !!!

---

Sunny, they asked in the question "NOT" correct sequence.

---

I am so sorry to bother you .. i knew i wasmissing something... Thank you so much Sir :-)

Answer 1

In Option D $\text{ b-c}$ with weight, $4$ is added before $\text{a-c}$ with weight $3$ is added. In Kruskal's algorithm, edges should be added in non-decreasing order of weight.

So, Option D may be correct.

Comments

Same is the case with (A) where (e,f) 5 is added before (a,c) 3

Then why is it not wrong ?

---

Option D

bcoz b-c (weight 4) is added before a-c (weight 3) ..In kruskal , weights are taken in ascending order..

---

@Sankaranarayanan P.N

> So option D may be correct

D is one of the correct option.

Answer 2

option d is right

Answer 3

Only sequence in option d is not possible..