The graph is given.

Graph as a hash:

graph = {
    0 => [1,9],
    1 => [0,8],
    2 => [3],
    3 => [2,4,5,7],
    4 => [3],
    5 => [3,6],
    6 => [5,7],
    7 => [3,6,11,10,8],
    8 => [1,7,9],
    9 => [0,8],
    10 => [7,11],
    11 => [7,10],
    12 => [],
}

Algorithm code with a loop instead of recursion

def dfs(graph, start_node)
  current_node = start_node
  stack = [start_node]
  visited = [start_node]
  loop do
    p "stack: #{stack}"
    p "visited: #{visited}"
    unvisited_neighbour = graph[current_node].find do |node|
      !visited.include?(node)
    end
    if unvisited_neighbour
      current_node = unvisited_neighbour
      visited << current_node
      stack << current_node
      next
    else
      stack.pop
      current_node = stack.last
      break unless current_node
    end
  end
end

dfs(graph, 0)