In this lab, we will focus on matrices and directed graphs represented as adjace

Question

In this lab, we will focus on matrices and directed graphs represented as adjacency matrices. It is highly recommended to use MATLAB for this lab. Roots and Leaves of a Graph Taking an adjacency matrix as input (matrix in MATLAB, 2d array in C++), return the set of roots and leaves in the graph. For example, in the graph below, the graph has roots 1, 2 and leaf 7. It is possible for a graph not to have roots and/or leaves. Determinant Write a function that takes as input a 2 times 2 matrix and a 3 times 3 matrix and outputs if the matrix is regular or singular. Implement two test cases for singular and regular.

Explanation / Answer

leaf_root.m

function [ ] = rootleaf( adj )
leaf=[];
root=[];
for i=1:size(adj,2)
flag=0;
for j=1:size(adj,1)
if(adj(j,i)==1)
flag=1;
end
end
if(flag==0)
root=[root i];
end
end
for i=1:size(adj,1)
flag=0;
for j=1:size(adj,2)
if(adj(i,j)==1)
flag=1;
end
end
if(flag==0)
leaf=[leaf i];
end
end
root
leaf   

end

Result:

>> adj=[0 0 1 0 0 0 0 0;0 0 1 0 0 0 0 0;0 0 0 1 1 0 0 0; 0 0 0 0 0 1 1 1;0 0 0 0 0 1 1 1;0 0 0 0 0 0 1 0;0 0 0 0 0 0 0 0;0 0 0 0 0 0 1 0;]

adj =

0 0 1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 1 0 0 0
0 0 0 0 0 1 1 1
0 0 0 0 0 1 1 1
0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0

>> rootleaf(adj)

root =

1 2

leaf =

7

2. Regular

function [ ] = regular( adj )
for i=1:size(adj,1)
for j=1:size(adj,2)
if(adj(i,j)==1)
adj(j,i)=1;
end
end
end
count=0;
flag=0;
for i=1:size(adj,1)
if(adj(1,i)==1)
count=count+1;
end
end
for i=2:size(adj,1)
count2=0;
for j=1:size(adj,2)
if(adj(i,j)==1)
count2=count2+1;
end
end
if(count2~=count)
flag=1;
end
end
if(flag==0)
disp('Matrix is regular');
else
disp('Matrix is not regular');
end
end

Result:

>> regular(adj)
Matrix is regular
>>

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