Q: 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
Solution: MultiGraphs and PseudoGraphs may have infinite number of edges, while 4 possible simple graphs exist.
Q: 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
Solution: In a uniform Graph all the hyper-edges have the same cardinality.
Q: What would be the Incidence Matrix of the given HyperGraph?
V = {x,y,z} E = {{x,y}{y}{x,z}{z,y}}
A. {{1,0,1,0},
{1,1,0,1},
{0,0,1,1}}
B. {{1,1,0,0},
{0,1,0,0},
{1,1,1,0}}
C. {{0,1,0,1},
{0,0,1,0},
{1,1,0,0}}
D. None of the Mentioned
Solution: The columns represent edges while rows represent vertices.
Q: 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
Solution: The degree of v1,v2,v3,v4,v5,v6 is 3,2,1,2,2,1 respectively.
Q: MultiGraphs having self-loops are called PseudoGraphs?
A. True
B. False
C. ....
D. ....
Solution: All PsuedoGraphs are MultiGraphs, but all MultiGraphs are not PseudoGraphs as all PseudoGraphs have self loop, but all MultiGraphs do not have self loops.