to finding the chromatic set

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Kajal Agrawal
Kajal Agrawal 2023-6-2
评论： Kajal Agrawal 2023-6-6
we want to chromatic number.
step1- creat a square matrix and first assign 0 in a set.
step 2- From the above matrix we select 1st vertex and assigned red color. Cut the row and column.
step 3- In the first cut row vertex with zero entry is 4 (vertex), so assign the same red color to it, and cut the corresponding row and column of vertex 4.
Step 4- Now in both the cut row no zero is left so we proceed to the next vertex 2 from the non-cut row assign the color green and cut the row and column 3 with the same color following the same steps. Finally, vertex 5 and 6 get colored with the third color. As shown in Figure 1 of Section 3.
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Kajal Agrawal
Kajal Agrawal 2023-6-4
移动：John D'Errico 2023-6-4

I want an algorithm. First, We create any square matrix and do some operations on it. select 1st vertex and assigned any color then Cut the row and column. In the first cut row vertex with zero (0) entry is in 4 (vertex), so assign the same color to it. Same step follow for the next vertex.next vertex is 2nd and assign the other color( green) and zeros is in 3rd vertex assign the same color (green) to it. At the end we have number of colors.

John D'Errico
John D'Errico 2023-6-4
You already HAVE the algorithm, as confusingly stated as it is. But as a pure question about an algorithm, this does not even belong on a MATLAB forum.

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回答（1 个）

Tushar
Tushar 2023-6-4
Hi Kajal,
I think you are trying to run the above algorithm on a matrix and trying to calculate the minimum number of different colors required to do so. If this is the case , in my opinion the following algorithm very closely does the same. But in this implementation, note two things:
  1. Cutting of any row or column is implemented by replacing the entries in that row or column by -1.
  2. Secondly, se calculating the answer from the length of the array "colors" which can contain duplicate values. SO in order to calculate unique values ,we can utilize the function "unique" and then count the number of elements by "numel".
  3. Also, I have initialized the matrix randomly. You can use the matrix in place of it for which you want to calculate the chromatic number.
function [matrix, num_colors] = simulate_procedure(n)
% Step 1: Initialize colors set
colors = [];
% Step 2: Create matrix and initialize with random values
matrix = randi([0, 1], n, n);
% Step 3: Assign color to the first vertex (vertex 1)
colors = [colors, 1];
color = 'red'; % Assign any color you like
% Step 4: Cut row and column of the first vertex
matrix(:, 1) = -1;
matrix(1, :) = -1;
% Step 5: Process remaining vertices
for vertex = 2:n
% Check if zero entry exists in the cut row of the current vertex
if any(matrix(vertex, :) == 0)
% Assign the same color as the previous vertex
colors = [colors, vertex];
if strcmp(color, 'red')
color = 'green';
else
color = 'red';
end
% Cut row and column of the current vertex
matrix(:, vertex) = -1;
matrix(vertex, :) = -1;
end
end
% Step 6: Number of colors used (after removing duplicates)
num_colors = numel(unique(colors));
end
% Usage example
n = 6;
[matrix, num_colors] = simulate_procedure(n);
disp('Matrix:');
disp(matrix);
disp(['Number of colors: ', num2str(num_colors)]);
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Kajal Agrawal
Kajal Agrawal 2023-6-6
i have run this code but shows "Function defination are not supported in this context"

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