Labelling nodes for undirected graph

I have the following issue in my code for L(2,1)-labelling problem. L(2,1)-labelling is to label positive integers to the nodes of graph such that

1) adjacent nodes receive value which differ by at least 2.

2) If the distance between the two nodes is 2 the difference between these nodes are 1.

my issue in the second loop

%this codes related to Njud Alotaibi (copy right)
function labellingcycles
%-----creating a graph-------
 s=[1 1 2 3 4];
 t=[2 3 4 5 5];
 G=graph(s,t);
 plot(G);
 %-----Sets--------
 S=[0,randperm(4)];
 Ver=[];
 x=[];
 % the first for loop here for first random labelling for the nodes 
    for i=1:5
       Ver(i)=S(i);
       Ver(:, i) = Ver(i);
    end
     Ver = Ver(:, 1:5) 
     
  % the second for loop to test the values in Ver set does it meet the  L(2,1)-labelling problem or not and 
  % store it in x set  
     for j=1:5
         % If conditions on the values should differen from their neighbors values and %
         % the difference between values should be 2 or more  
         if (Ver(j)~= Ver(neighbors(G,j)))  & (abs(Ver(j)-Ver(neighbors(G,j)))>=2) 
             x(j)=Ver(j);
             x(:, j) = x(j); 
             % if does not meet the condition i need to change the value to
             % meet the condition but how 
         else
             break % break becuse i just need to change the value that does not meet the condition 
             end 
         end 
     x = x(:, 1:5)
end

Answer 1

[ag]

Hi Njud,

I understand that you need to label your graph as per the below stated conditions:

1. Value for the adjacent nodes should differ by at least 2.
2. Value for nodes with distance 2, should differ by 1.

To do so, you will have to use recursion or stack for implementing a graph traversal algorithm(BFS should be of help).

Please refer to the following documentation of “bfsearch”, which is an in-built function for BFS,

Breadth-first graph search - MATLAB bfsearch - MathWorks India

Hope this helps!

Best Regards,

Aryan Gupta