Network Theory Multiple Choice Questions on “Tree and Co-Tree”.
1. A graph is said to be a directed graph if ________ of the graph has direction.
A. 1 branch
B. 2 branches
C. 3 branches
D. every branch
Answer: D
Clarification: If every branch of the graph has direction, then the graph is said to be a directed graph. If the graph does not have any direction then that graph is called undirected graph.
2. The number of branches incident at the node of a graph is called?
A. degree of the node
B. order of the node
C. status of the node
D. number of the node
Answer: A
Clarification: Nodes can be incident to one or more elements. The number of branches incident at the node of a graph is called degree of the node.
3. If no two branches of the graph cross each other, then the graph is called?
A. directed graph
B. undirected graph
C. planar graph
D. non-planar graph
Answer: C
Clarification: If a graph can be drawn on a plane surface such that no two branches of the graph cross each other, then the graph is called planar graph.
4. Consider the graph given below. Which of the following is a not a tree to the graph?
Answer: D
Clarification: Tree is sub graph which consists of all node of original graph but no closed paths. So, ‘d’ is not a tree to the graph.
5. Number of twigs in a tree are? (where, n-number of nodes)
A. n
B. n+1
C. n-1
D. n-2
Answer: C
Clarification: Twig is a branch in a tree. Number of twigs in a tree are n-1. If there are 4 nodes in a tree then number of possible twigs are 3.
6. Loops which contain only one link are independent are called?
A. open loops
B. closed loops
C. basic loops
D. none of the mentioned
Answer: C
Clarification: The addition of subsequent link forms one or more additional loops. Loops that contain only one link are independent are called basic loops.
7. If the incident matrix of a graph is given below. The corresponding graph is?
a b c d e f
1 +1 0 +1 0 0 +1
2 -1 -1 0 +1 0 0
3 0 +1 0 0 +1 -1
4 0 0 -1 -1 -1 0
A.
Answer: B
Clarification: For the given incidence matrix,
a b c d e f
1 +1 0 +1 0 0 +1
2 -1 -1 0 +1 0 0
3 0 +1 0 0 +1 -1
4 0 0 -1 -1 -1 0
the corresponding graph is
considering the directions specified in the graph.
8. If A represents incidence matrix, I represents branch current vectors, then?
A. AI = 1
B. AI = 0
C. AI = 2
D. AI= 3
Answer: B
Clarification: If A represents incidence matrix, I represents branch current vectors, then the relation is AI= 0 that is its characteristic equation must be equated to zero
9. If a graph consists of 5 nodes, then the number of twigs in the tree is?
A. 1
B. 2
C. 3
D. 4
Answer: D
Clarification: Number of twigs = n-1. As given number of nodes are 5 then n = 5. On substituting in the equation, number of twigs = 5 -1 = 4.
10. If there are 4 branches, 3 nodes then number of links in a co-tree are?
A. 2
B. 4
C. 6
D. 8
Answer: A
Clarification: Number of links = b-n+1. Given number of branches = 4 and number of nodes = 3. On substituting in the equation, number of links in a co-tree = 4 – 3 + 1 = 2.