code: def is_vertex_coloring(G, coloring):
      
      return all(coloring[u] != coloring[v] for u, v in G.edges)
docs: Determines whether the given coloring is a vertex coloring of graph G.
  
      Parameters
      ----------
      G : NetworkX graph
          The graph on which the vertex coloring is applied.
  
      coloring : dict
          A coloring of the nodes of G. Should be a dict of the form
          {node: color, ...}.
  
      Returns
      -------
      is_vertex_coloring : bool
          True if the given coloring defines a vertex coloring; that is, no
          two adjacent vertices share a color.
  
      Example
      -------
      This example colors checks two colorings for a graph, G, of a single Chimera
      unit cell. The first uses one color (0) for the four horizontal qubits
      and another (1) for the four vertical qubits, in which case there are
      no adjacencies; the second coloring swaps the color of one node.
  
      >>> G = dnx.chimera_graph(1,1,4)
      >>> colors = {0: 0, 1: 0, 2: 0, 3: 0, 4: 1, 5: 1, 6: 1, 7: 1}
      >>> dnx.is_vertex_coloring(G, colors)
      True
      >>> colors[4]=0
      >>> dnx.is_vertex_coloring(G, colors)
      False