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Test: Graph Theory- 2 - Question 1

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: Graph Theory- 2 - Question 2

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

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Test: Graph Theory- 2 - Question 3

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: Graph Theory- 2 - Question 4

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: Graph Theory- 2 - Question 7

G is a simple, connected, undirected graph. Some vertices of G are of odd degree. Add a node v to G and make it adjacent to each odd degree vertex of G. The resultant graph is sure to be

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Test: Graph Theory- 2 - Question 8

The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?

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Test: Graph Theory- 2 - Question 10

Which of the following statements is/are TRUE for undirected graph?

P: Number of odd degree vertices is even.

Q: Sum of degrees of all vertices is even.

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Test: Graph Theory- 2 - Question 11

An ordered n-tuple (d_{1}, d_{2}, .... d_{n}) with d_{1} ≥ d_{2 }≥ ... ≥ d_{n} is called graphic if there exists a simple undirected graph with n vertices having degrees d_{1}, d_{2}, ..., d_{n} respectively. Which of the following 6-tuples is NOT graphic?

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Test: Graph Theory- 2 - Question 12

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

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