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Free download in PDF Graph Theory Short Questions and Answers for competitive exams. These short objective type questions with answers are very important for Board exams as well as competitive exams. These short solved questions or quizzes are provided by Gkseries.
41
An undirected graph possesses an eulerian circuit if and only if it is connected and its vertices are
[A]
all of even degree
[B]
all of odd degree
[C]
of any degree
[D]
even in number
Answer: all of even degree
42
The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is
[A]
Reflexive
[B]
Transitive
[C]
Symmetric
[D]
None of these
43
In an undirected graph the number of nodes with odd degree must be
[A]
Zero
[B]
Odd
[C]
Prime
[D]
Even
44
What is the probability of choosing correctly an unknown integer between 0 and 9 with 3 chances ?
[A]
963/1000
[B]
966/1000
[C]
968/1000
[D]
None of these
45
The complete graph K, has... different spanning trees?
[A]
nn-2
[B]
n*n
[C]
nn
[D]
n2
46
Eccentricity of a vertex denoted by e(v) is defined by.... ?
[A]
max { d(u,v): u belongs to v, u does not equal to v : where d(u,v) is the distance between u&v}
[B]
min { d(u,v): u belongs to v, u does not equal to v }
[C]
Both A and B
[D]
None of these
Answer: max { d(u,v): u belongs to v, u does not equal to v : where d(u,v) is the distance between u&v}
47
A graph G is called a ..... if it is a connected acyclic graph ?
[A]
Cyclic graph
[B]
Regular graph
[C]
Tree
[D]
Not a graph
48
Length of the walk of a graph is .... ?
[A]
The number of vertices in walk W
[B]
The number of edges in walk W
[C]
Total number of edges in a graph
[D]
Total number of vertices in a graph
Answer: The number of edges in walk W
49
If for some positive integer k, degree of vertex d(v)=k for every vertex v of the graph G, then G is called... ?
[A]
K graph
[B]
K-regular graph
[C]
Empty graph
[D]
All of above
50
The number of colours required to properly colour the vertices of every planer graph is
51
In how many ways can a president and vice president be chosen from a set of 30 candidates?
[A]
820
[B]
850
[C]
880
[D]
870
52
Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is ½. What is the expected number of unordered cycles of length three?
[A]
1/8
[B]
1
[C]
7
[D]
3
53
In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities?
[A]
100
[B]
120
[C]
110
[D]
150
54
The number of colours required to properly color vertices of every planar graph is
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