code: def mycielskian(G, iterations=1):
      r"""Returns the Mycielskian of a simple, undirected graph G
  
      The Mycielskian of graph preserves a graph's triangle free
      property while increasing the chromatic number by 1.
  
      The Mycielski Operation on a graph, :math:`G=(V, E)`, constructs a new
      graph with :math:`2|V| + 1` nodes and :math:`3|E| + |V|` edges.
  
      The construction is as follows:
  
      Let :math:`V = {0, ..., n-1}`. Construct another vertex set
      :math:`U = {n, ..., 2n}` and a vertex, `w`.
      Construct a new graph, `M`, with vertices :math:`U \bigcup V \bigcup w`.
      For edges, :math:`(u, v) \in E` add edges :math:`(u, v), (u, v + n)`, and
      :math:`(u + n, v)` to M. Finally, for all vertices :math:`u \in U`, add
      edge :math:`(u, w)` to M.
  
      The Mycielski Operation can be done multiple times by repeating the above
      process iteratively.
  
      More information can be found at https://en.wikipedia.org/wiki/Mycielskian
  
      Parameters
      ----------
      G : graph
          A simple, undirected NetworkX graph
      iterations : int
          The number of iterations of the Mycielski operation to
          perform on G. Defaults to 1. Must be a non-negative integer.
  
      Returns
      -------
      M : graph
          The Mycielskian of G after the specified number of iterations.
  
      Notes
      -----
      Graph, node, and edge data are not necessarily propagated to the new graph.
  
      """
  
      M = nx.convert_node_labels_to_integers(G)
  
      for i in range(iterations):
          n = M.number_of_nodes()
          M.add_nodes_from(range(n, 2 * n))
          old_edges = list(M.edges())
          M.add_edges_from((u, v + n) for u, v in old_edges)
          M.add_edges_from((u + n, v) for u, v in old_edges)
          M.add_node(2 * n)
          M.add_edges_from((u + n, 2 * n) for u in range(n))
  
      return M
  
imports: import networkx
  from networkx.utils import not_implemented_for
label_desc: Use image node_id 1 for calling a global function with example usage: mycielskian(G, iterations) and returns: M