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Suppose I color the vertices of a graph properly, and I wish to obtain thertex, where color code for each vertex is defined as a tuple of the color of the vertex along with number of neighbors with each color to the vertex. How do I get at that? Will all_graph_colorings or first_coloring help in that: Some pseudo code beginning would be:

 from sage.graphs.graph_coloring import first_coloring
 G = graphs.WheelGraph(5)
 d=first_coloring(G, 5)
 l=[]
 for i in G.vertices():
      for j in G.neighbors(i):
           l.append(d[i],d[j])
 return l

In the above code, I think there are several problems. First, the double iteration might not produce the tuple that I want as I have mentioned only pairs to be appended to the list l. Next, on running the code, I get the error append method only takes one argument and two are given. How do I fix that? The color code concept is inspired from the irregular chromatic number of the graph explained in some detail here. Any ideas? Thanks beforehand.

Suppose I color the vertices of a graph properly, and I wish to obtain thertex, the color code for each vertex, where color code color code for each vertex is defined as a tuple of the color of the vertex along with number of neighbors with corresponding to each color to the vertex. How do I get at that? Will all_graph_colorings or first_coloring help in that: Some pseudo code using first_coloring beginning would be:

 from sage.graphs.graph_coloring import first_coloring
 G = graphs.WheelGraph(5)
 d=first_coloring(G, 5)
 l=[]
 for i in G.vertices():
      for j in G.neighbors(i):
           l.append(d[i],d[j])
 return l

In the above code, I think there are several problems. First, First of all, the first_coloring does not cover all possible colorings. Next, the double iteration might not produce the tuple that I want as I have mentioned only pairs to be appended to the list l. Next, Again, on running the code, I get the error append method only takes one argument and two are given. How do I fix that? The color code concept is inspired from the irregular chromatic number of the graph explained in some detail here. Any ideas? Thanks beforehand.

Suppose I color the vertices of a graph properly, and I wish to obtain the color code for each vertex, where color code for each vertex is defined as a tuple of the color of the vertex along with number of neighbors corresponding to each color to the vertex. How do I get at that? Will all_graph_colorings or first_coloring help in that: Some pseudo code using first_coloring beginning would be:

 from sage.graphs.graph_coloring import first_coloring
 G = graphs.WheelGraph(5)
 d=first_coloring(G, 5)
 l=[]
 for i in G.vertices():
      for j in G.neighbors(i):
           l.append(d[i],d[j])
 return l

In the above code, I think there are several problems. First of all, the first_coloring does not cover all possible colorings. colorings and is a list and not a dictionary. The all_graph_colorings though gives a dictionary, but I am unsure of how to access the elements there. Next, the double iteration might not produce the tuple that I want as I have mentioned only pairs to be appended to the list l. Again, on running the code, I get the error append method only takes one argument and two are given. How do I fix that? The color code concept is inspired from the irregular chromatic number of the graph explained in some detail here. Any ideas? Thanks beforehand.

Suppose I color the vertices of a graph properly, and I wish to obtain the color code for each vertex, where color code for each vertex is defined as a tuple of the color of the vertex along with number of neighbors corresponding to each color to the some vertex. How do I get at that? Will all_graph_colorings or first_coloring help in that: Some pseudo code using first_coloring beginning would be:

 from sage.graphs.graph_coloring import first_coloring
 G = graphs.WheelGraph(5)
 d=first_coloring(G, 5)
 l=[]
 for i in G.vertices():
      for j in G.neighbors(i):
           l.append(d[i],d[j])
 return l

In the above code, I think there are several problems. First of all, the first_coloring does not cover all possible colorings and is a list and not a dictionary. The all_graph_colorings though gives a dictionary, but I am unsure of how to access the elements there. Next, the double iteration might not produce the tuple that I want as I have mentioned only pairs to be appended to the list l. Again, on running the code, I get the error append method only takes one argument and two are given. How do I fix that? The color code concept is inspired from the irregular chromatic number of the graph explained in some detail here. Any ideas? Thanks beforehand.