GATE CSE 2021 Set 2 | Greedy Method Question 6 | Algorithms

GATE CSE 2021 Set 2

MCQ (Single Correct Answer)

-0.33

Let G be a connected undirected weighted graph. Consider the following two statements.

S₁: There exists a minimum weight edge in G which is present in every minimum spanning tree of G.

S₂: If every edge in G has distinct weight, then G has a unique minimum spanning tree. Which one of the following options is correct?

S1 is false and S2 is true.

S1 is true and S2 is false.

Both S1 and S2 are true.

Both S1 and S2 are false.

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

Let $$G$$ be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increased by the same value, then which of the following statements is/are TRUE?

$$P:$$ Minimum spanning tree of $$G$$ does not change
$$Q:$$ Shortest path between any pair of vertices does not change

$$P$$ only

$$Q$$ only

Neither $$P$$ nor $$Q$$

Both $$P$$ and $$Q$$

GATE CSE 2006

MCQ (Single Correct Answer)

-0.3

To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure to be used is:

Queue

Stack

Heap

B-Tree

GATE CSE 2006

MCQ (Single Correct Answer)

-0.3

Consider a weighted complete graph G on the vertex set {v1, v2, ..vn} such that the weight of the edge (vi, vj) is $$2|i-j|$$. The weight of a minimum spanning tree of G is:

n — 1

2n — 2

$${n \over 2}$$

$$n^2$$