<｜begin▁of▁sentence｜>### Instruction:
As a Safety Consultant, you've been asked to use your knowledge of networkx to style a binary tree graph in igraph and set the background color of the plot to light blue using CairoPlot. Additionally, you've been requested to save the visual output to an image file named 'tree_with_background.png' with the specified background color.
### Response:
import igraph as ig
from igraph import plot

# Construct the graph
g = ig.Graph.Tree(127, 2)
g.vs['label'] = range(127)

# Define layout for plotting
g_layout = g.layout('rt')

# Create CairoPlot instance and set background color
cairo_plot = plot(g, layout=g_layout, bbox=(600, 600), margin=50)
cairo_plot.background = ig.drawing.colors.color_name_to_rgb('lightblue')

# Save the plot to a file
cairo_plot.save('tree_with_background.png')
<|EOT|>
