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Multigraph and Hypergraph MCQs
1. 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
Answer: There exists a MultiGraph having 10 vertices such that minimum degree of the graph is 0 and maximum degree is 9
2. 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)
Answer: i) and iii)
3. Possible number of labelled simple Directed, Pseudo and Multigarphs exist having 2 vertices?
a) 3, Infinite, 4
b) 4, 3, Infinite
c) 4, Infinite, infinite
d) 4, Infinite, Infinite
Answer: 4, Infinite, Infinite
4. Which of the following is a HyperGraph, where V is the set of vertices, E is the set of edges?
a) V = {v1, v2, v3} E = {e1, e2} = {{v2, v3} {v1, v3}}
b) V = {v1, v2} E = {e1} = {{v1, v2}}
c) V = {v1, v2, v3} E = {e1, e2, e3} = {{v2, v3}{v3, v1}{v2, v1}}
d) All of the mentioned
Answer: All of the mentioned
5. What is the degree sequence of the given HyperGraph, in non-increasing order.
V = {v1,v2,v3,v4,v5,v6} E = {{v1,v4,v5} {v2,v3,v4,v5} {v2} {v1} {v1,v6}}
a) 3,2,1,1,1,1
b) 3,2,2,2,1,1
c) 3,2,2,2,2,1
d) 3,2,2,1,1,1
Answer: 3,2,2,2,1,1
6. MultiGraphs having self-loops are called PseudoGraphs?
a) True
b) False
Answer: True
7. 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)
Answer: i) and iii)
8. All undirected Multigraphs contain eulerian cycles.
a) True
b) False
Answer: True
9. 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
Answer: 6