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Test: Graphs Theory- 2 - Question 1

If G is a forest with n vertices and k connected components, how many edges does G have?

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Test: Graphs Theory- 2 - Question 2

Let d denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices with d ≥ 3, which one of the following is TRUE?

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Test: Graphs Theory- 2 - Question 3

The 2^{n} vertices of a graph G corresponds to all subsets of a set of size n, for n >= 6 . Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of vertices of degree zero in G is:

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Test: Graphs Theory- 2 - Question 4

The 2^{n} vertices of a graph G corresponds to all subsets of a set of size n, for n >= 6. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in G is:

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Test: Graphs Theory- 2 - Question 5

Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is

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Test: Graphs Theory- 2 - Question 6

Let G be a simple graph with 20 vertices and 100 edges. The size of the minimum vertex cover of G is 8. Then, the size of the maximum independent set of G is

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Test: Graphs Theory- 2 - Question 8

Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?

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Test: Graphs Theory- 2 - Question 9

The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same colour, is

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Test: Graphs Theory- 2 - Question 10

Let G be an arbitrary graph with n nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie between

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Test: Graphs Theory- 2 - Question 11

How many perfect matchings are there in a complete graph of 6 vertices ?

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Test: Graphs Theory- 2 - Question 12

A graph G = (V, E) satisfies |E| ≤ 3 |V| - 6. The min-degree of G is defined as

Therefore, min-degree of G cannot be

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Test: Graphs Theory- 2 - Question 13

The minimum number of colours required to colour the vertices of a cycle with η nodes in such a way that no two adjacent nodes have the same colour is

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Test: Graphs Theory- 2 - Question 14

Maximum number of edges in a n - node undirected graph without self loops is

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Test: Graphs Theory- 2 - Question 15

Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is _______________.

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Test: Graphs Theory- 2 - Question 16

A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on n vertices, n is

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Test: Graphs Theory- 2 - Question 17

In a connected graph, a bridge is an edge whose removal disconnects a graph. Which one of the following statements is True?

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Test: Graphs Theory- 2 - Question 18

What is the number of vertices in an undirected connected graph with 27 edges, 6 vertices of degree 2, 3 vertices of degree *4* and remaining of degree 3?

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Test: Graphs Theory- 2 - Question 19

The minimum number of colours that is sufficient to vertex-colour any planar graph is _______________

[This Question was originally a Fill-in-the-blanks Question]

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Test: Graphs Theory- 2 - Question 20

If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is a

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