221.  Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is _______________. 
a.  24 
b.  20 
c.  32 
d.  64 
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Answer: (a).24

222.  A graph is selfcomplementary if it is isomorphic to its complement. For all selfcomplementary graphs on n vertices, n is 
a.  A multiple of 4 
b.  Even 
c.  Odd 
d.  Congruent to 0 mod 4, or 1 mod 4 
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Answer: (d).Congruent to 0 mod 4, or 1 mod 4

223.  In a connected graph, a bridge is an edge whose removal disconnects a graph. Which one of the following statements is True? 
a.  A tree has no bridge 
b.  A bridge cannot be part of a simple cycle 
c.  Every edge of a clique with size ≥ 3 is a bridge (A clique is any complete subgraph of a graph) 
d.  A graph with bridges cannot have a cycle 
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Answer: (b).A bridge cannot be part of a simple cycle

224.  What is the number of vertices in an undirected connected graph with 27 edges, 6 vertices of degree 2, 3 vertices of degree 4 and remaining of degree 3? 
a.  10 
b.  11 
c.  18 
d.  19 
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Answer: (d).19

225.  The minimum number of colours that is sufficient to vertexcolour any planar graph is _______________. 
a.  1 
b.  2 
c.  3 
d.  4 
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Answer: (d).4

226.  If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is a 
a.  Hamiltonian cycle 
b.  grid 
c.  hypercube 
d.  tree 
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Answer: (d).tree

227.  Consider a weighted undirected graph with positive edge weights and let uv be an edge in the graph. It is known that the shortest path from the source vertex s to u has weight 53 and the shortest path from s to v has weight 65. Which one of the following statements is always true? 
a.  weight (u, v) < 12 
b.  weight (u, v) ≤ 12 
c.  weight (u, v) > 12 
d.  weight (u, v) ≥ 12 
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Answer: (d).weight (u, v) ≥ 12

228.  What is the chromatic number of the following graph? 
a.  2 
b.  3 
c.  4 
d.  5 
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Answer: (b).3

229.  G is a simple undirected graph. Some vertices of G are of odd degree. Add a node v to G and make it adjacent to each odd degree vertex of G. The resultant graph is sure to be 
a.  regular 
b.  Complete 
c.  Hamiltonian 
d.  Euler 
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Answer: (d).Euler
