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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