21.  A connected graph T without any cycles is called ........ 
a.  free graph 
b.  no cycle graph 
c.  non cycle graph 
d.  circular graph 
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Answer: (a).free graph

22.  In a graph if E=(u,v) means ...... 
a.  u is adjacent to v but v is not adjacent to u 
b.  e begins at u and ends at v 
c.  u is processor and v is successor 
d.  both b and c 
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Answer: (d).both b and c

23.  Let G = (V, E) be any connected undirected edgeweighted graph. The weights of the edges in E are positive any distinct. Consider the following statements:
I. Minimum Spanning Tree of G is always unique. II. Shortest path between any two vertices of G is always unique. Which of the above statements is/are necessarily true? 
a.  I only 
b.  II only 
c.  both I and II 
d.  neither I and II 
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Answer: (a).I only

24.  Let A be an adjacency matrix of a graph G. The ij th entry in the matrix Ak , gives 
a.  The number of paths of length K from vertex Vi to vertex Vj. 
b.  Shortest path of K edges from vertex Vi to vertex Vj. 
c.  Length of a Eulerian path from vertex Vi to vertex Vj. 
d.  Length of a Hamiltonian cycle from vertex Vi to vertex Vj. 
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Answer: (b).Shortest path of K edges from vertex Vi to vertex Vj.

25.  For an undirected graph with n vertices and e edges, the sum of the degree of each vertex is equal to 
a.  2n 
b.  (2n1)/2 
c.  2e 
d.  4n 
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Answer: (c).2e

26.  An undirected graph G with n vertices and e edges is represented by adjacency list. What is the time required to generate all the connected components?

a.  O (n) 
b.  O (e) 
c.  O (e+n) 
d.  O (en) 
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Answer: (c).O (e+n)

27.  A graph with n vertices will definitely have a parallel edge or self loop if the total number of edges are 
a.  more than n 
b.  more than n 
c.  more than (n+1)/2 
d.  more than n(n1)/2 
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Answer: (d).more than n(n1)/2

28.  The maximum degree of any vertex in a simple graph with n vertices is 
a.  n–1 
b.  n+1 
c.  2n–1 
d.  n 
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Answer: (a).n–1

29.  The data structure required for Breadth First Traversal on a graph is 
a.  queue 
b.  stack 
c.  array 
d.  tree 
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Answer: (a).queue

30.  In Breadth First Search of Graph, which of the following data structure is used? 
a.  Stack 
b.  Queue 
c.  Linked List 
d.  None of the above 
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Answer: (b).Queue
