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I have drawn some graphs within the notbook mupad and have found their chromatic numbers. Is it possible to then find their total chromatic numbers?

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For example the total chromatic number for the following graph:
HG1 := Graph([a, b, c, d], [[a, b], [b, c], [b, d], [a, c], [a, d], [c, d]], Undirected):
vOrder := [None, None, None, None, None, None, a, None, None, None, None, None, None, None, None, None, None, None, b, None, None, None, None, None, None, None, c, None, None, None, None, None, None, d, None, None ]:
plot(Graph::plotGridGraph(HG1, VerticesPerLine = 12, VertexOrder = vOrder))

Answers (1)

Jaynik
Jaynik on 5 Sep 2024
Hi Olivia,
You can use a simple greedy algorithm to find the color of each vertex in MATLAB. Following is a sample code for the same:
% Sample graph input
s = [1 1 2 2 3 4 4 5 5 6 7 8];
t = [2 4 3 5 6 5 7 6 8 9 8 9];
G = graph(s, t);
plot(G);
% Find the chromatic number (vertex coloring) using a greedy algorithm
numNodes = numnodes(G);
vertexColors = zeros(numNodes, 1);
for i = 1:numNodes
neighborColors = vertexColors(neighbors(G, i));
availableColors = setdiff(1:numNodes, neighborColors);
vertexColors(i) = availableColors(1);
end
disp('Vertex Colors:');
disp(vertexColors);
For migrating MuPAD notebooks to MATLAB live script, please refer the following MATLAB Answer:
Hope this helps!

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