<｜begin▁of▁sentence｜>### Instruction:
Given a tree graph with 3 levels and a branching factor of 2, how can you visualize its vertices using igraph's CairoVertexDrawer, and subsequently save the drawing to a PNG file?
### Response:
import igraph as ig
import cairo

# Create a graph
graph = ig.Graph.Tree(3, 2)

# Create a layout for the graph
g_layout = graph.layout('auto')

# Create a surface to draw on and a drawing context
surface = cairo.ImageSurface(cairo.FORMAT_ARGB32, 600, 400)
context = cairo.Context(surface)

# Define a bounding box
bbox = ig.drawing.BoundingBox(600, 400)

# Define a palette
colors = ig.drawing.colors.ClusterColoringPalette(20)

# Construct the vertex drawer
vertex_drawer = ig.drawing.vertex.CairoVertexDrawer(context=context, bbox=bbox, palette=colors, layout=g_layout)

# Draw the vertices of the graph
for idx, vertex in enumerate(graph.vs):
    vertex_drawer.draw(visual_vertex=graph._coerce_vertex(vertex), vertex=vertex, coords=g_layout[idx])

# Save the result to a PNG file
surface.write_to_png('tree_graph.png')
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