71. In the given connected graph G, what is the value of rad(G) and diam(G)?
a. 2, 3
b. 3, 2
c. 2, 2
d. 3, 3
Answer: (a).2, 3

72. Which of these adjacency matrices represents a simple graph?
a. [ [1, 0, 0], [0, 1, 0], [0, 1, 1] ]
b. [ [1, 1, 1], [1, 1, 1], [1, 1, 1] ]
c. [ [0, 0, 1], [0, 0, 0], [0, 0, 1] ]
d. [ [0, 0, 1], [1, 0, 1], [1, 0, 0] ]
Answer: (d).[ [0, 0, 1], [1, 0, 1], [1, 0, 0] ]

73. Given an adjacency matrix A = [ [0, 1, 1], [1, 0, 1], [1, 1, 0] ], how many ways are there in which a vertex can walk to itself using 2 edges.
a. 2
b. 4
c. 6
d. 8
Answer: (c).6

74. If A[x+3][y+5] represents an adjacency matrix, which of these could be the value of x and y.
a. x=5, y=3
b. x=3, y=5
c. x=3, y=3
d. x=5, y=5
Answer: (a).x=5, y=3

75. Two directed graphs(G and H) are isomorphic if and only if A=PBP-1, where P and A are adjacency matrices of G and H respectively.
a. True
b. False
c. May be
d. Can't say
Answer: (a).True

76. Given the following program, what will be the 3rd number that’d get printed in the output sequence for the given input?
#include <bits/stdc++.h> 
using namespace std; 
int cur=0; 
int G[10][10]; 
bool visited[10]; 
deque <int> q; 
 
void fun(int n); 
 
int main()
{   
 int num=0; 
 int n; 
 cin>>n; 
 
 for(int i=0;i<n;i++) 
       for(int j=0;j<n;j++) 
         cin>>G[i][j]; 
 
 for(int i=0;i<n;i++) 
        visited[i]=false; 
 
        fun(n); 
 return 0; 
} 
 
void fun(int n)
{ 
 cout<<cur<<" "; 
 visited[cur]=true; 
 q.push_back(cur); 
 
 do
        { 
  for(int j=0;j<n;j++)
                { 
      if(G[cur][j]==1 && !visited[j])
                    { 
          q.push_back(j); 
          cout<<j<<" "; 
          visited[j]=true; 
             } 
 
                 } 
 
  q.pop_front(); 
  if(!q.empty()) 
  cur=q.front(); 
  }while(!q.empty()); 
}


Input Sequence:-

9 
0 1 0 0 0 0 0 0 1    
1 0 0 0 0 0 0 0 0 
0 0 0 1 1 1 0 0 1 
0 0 1 0 0 0 0 0 0 
0 0 1 0 0 0 0 1 0 
0 0 1 0 0 0 1 0 0 
0 0 0 0 0 1 0 1 1 
0 0 0 0 1 0 1 0 0 
1 0 1 0 0 0 1 0 0
a. 2
b. 6
c. 8
d. 4
Answer: (c).8

77. For which type of graph, the given program would run infinitely? The Input would be in the form of an adjacency Matrix and n is its dimension (1<n<10).
#include <bits/stdc++.h> 
using namespace std; 
int G[10][10]; 
void fun(int n); 
 
int main()
{
 int num=0; 
 int n; 
 cin>>n; 
 for(int i=0;i<n;i++) 
   for(int j=0;j<n;j++) 
          cin>>G[i][j]; 
     fun(n); 
 return 0; 
}  
 
void fun(int n)
{ 
 for(int i=0;i<n;i++) 
 for(int j=0;j<n;j++) 
 if(G[i][j]==1) 
 j--; 
}
a. All Fully Connected Graphs
b. All Empty Graphs
c. All Bipartite Graphs
d. None of the Mentioned
Answer: (b).All Empty Graphs

78. Given the following adjacency matrix of a graph(G) determine the number of components in the G.

[0 1 1 0 0 0],

[1 0 1 0 0 0],

[1 1 0 0 0 0],

[0 0 0 0 1 0],

[0 0 0 1 0 0],

[0 0 0 0 0 0].
a. 1
b. 2
c. 3
d. 4
Answer: (c).3

79. Incidence matrix and Adjacency matrix of a graph will always have same dimensions?
a. True
b. False
c. May be
d. Can't say
Answer: (b).False

80. The column sum in an incidence matrix for a simple graph is __________
a. depends on number of edges
b. always greater than 2
c. equal to 2
d. equal to the number of edges
Answer: (c).equal to 2