code: def dominating_set(G, start_with=None):
      r"""Finds a dominating set for the graph G.
  
      A *dominating set* for a graph with node set *V* is a subset *D* of
      *V* such that every node not in *D* is adjacent to at least one
      member of *D* [1]_.
  
      Parameters
      ----------
      G : NetworkX graph
  
      start_with : node (default=None)
          Node to use as a starting point for the algorithm.
  
      Returns
      -------
      D : set
          A dominating set for G.
  
      Notes
      -----
      This function is an implementation of algorithm 7 in [2]_ which
      finds some dominating set, not necessarily the smallest one.
  
      See also
      --------
      is_dominating_set
  
      References
      ----------
      .. [1] https://en.wikipedia.org/wiki/Dominating_set
  
      .. [2] Abdol-Hossein Esfahanian. Connectivity Algorithms.
          http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
  
      """
      all_nodes = set(G)
      if start_with is None:
          start_with = arbitrary_element(all_nodes)
      if start_with not in G:
          raise nx.NetworkXError(f"node {start_with} is not in G")
      dominating_set = {start_with}
      dominated_nodes = set(G[start_with])
      remaining_nodes = all_nodes - dominated_nodes - dominating_set
      while remaining_nodes:
          # Choose an arbitrary node and determine its undominated neighbors.
          v = remaining_nodes.pop()
          undominated_nbrs = set(G[v]) - dominating_set
          # Add the node to the dominating set and the neighbors to the
          # dominated set. Finally, remove all of those nodes from the set
          # of remaining nodes.
          dominating_set.add(v)
          dominated_nodes |= undominated_nbrs
          remaining_nodes -= undominated_nbrs
      return dominating_set
  
imports: from itertools import chain
  import networkx
  from networkx.utils import arbitrary_element
label_desc: Use image node_id 1 for calling a global function with example usage: dominating_set(G, start_with) and returns: dominating_set