Test Series - Data Structure

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Test Number 115/115

Q: Consider the following symbols and choose which of the symbols represent nodes having atleast one child?

i) Δ ii) ◊ iii) ∇ iv) T v) ⊥
A. iv) and v)
B. iii) iv) and v)
C. i) and ii)
D. i) and iii)
Solution: The symbols Δ and ◊ represents logical AND and OR gates.
Q: Which of the following symbols represent nodes having exactly one child?

i) Δ ii) ◊ iii) ∇ iv) T v) ⊥
A. iv) and v)
B. v)
C. i) and iii)
D. iii)
Solution: ∇ symbol represents the logical NOT gate.
Q: Which of the following symbols represent leaf nodes?

i) Δ ii) ◊ iii) ∇ iv) T v) ⊥
A. iv) and v)
B. v)
C. i) and iii)
D. ii)
Solution: The two symbols T, ⊥ represent the Boolean values.
Q: Every Binary Decision Diagram is also a Propositional Directed Acyclic Graph.
A. True
B. False
C. ...
D. ...
Solution: Both Binary Decision Diagram and Propositional Directed Acyclic Graph may be used to represent the same Boolean function.
Q: In a Propositional Directed Acyclic Graph Leaves maybe labelled with a boolean variable.
A. True
B. False
C. ...
D. ...
Solution: In a Propositional Directed Acyclic Graph leaves maybe labelled with a boolean variable, T or ⊥.
Q: Given Adjacency matrices determine which of them are PseudoGraphs?
i) {{1,0} {0,1}}
ii) {{0,1}{1,0}}
iii) {{0,0,1}{0,1,0}{1,0,0}}
A. only i)
B. ii) and iii)
C. i) and iii)
D. i) ii) and iii)
Solution: In i) self loops exist for both the vertices, in iii) self loop exists in the second vertex.
Q: All undirected Multigraphs contain eulerian cycles.
A. True
B. False
C. ...
D. ...
Solution: Only graphs with every vertex having even degree have eulerian circuits or cycles.
Q: Determine the number of vertices for the given Graph or Multigraph?
G is a 4-regular Graph having 12 edges.
A. 3
B. 6
C. 4
D. Information given is insufficient
Solution: Sum of degrees of all the edges equal to 2 times the number of edges. 2*12=4*n, n=>6.
Q: Which of the following statement is true.
A. There exists a Simple Graph having 10 vertices such that minimum degree of the graph is 0 and maximum degree is 9
B. There exists a MultiGraph having 10 vertices such that minimum degree of the graph is 0 and maximum degree is 9
C. There exists a MultiGraph as well as a Simple Graph having 10 vertices such that minimum degree of the graph is 0 and maximum degree is 9
D. None of the mentioned
Solution: If a vertex has a degree 9 that means it is connected to all the other vertices, in case of Multigraphs for an isolate vertex, and a multiple edge may compensate.
Q: Given Adjacency matrices determine which of them are PseudoGraphs?
i) {{1,0} {0,1}}
ii) {{0,1}{1,0}}
iii) {{0,0,1}{0,1,0}{1,0,0}}
A. only i)
B. ii) and iii)
C. i) and iii)
D. i) ii) and iii)
Solution: In i) self loops exist for both the vertices, in iii) self loop exists in the second vertex.

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