Let 
be a simple graph on vertex
set 
and let 
be a subset of 
. Two vertices 
are called "
-visible" if there exists a shortest
path from 
to 
such that none of the internal vertices on the path belong to 
. A set 
is then called a mutual-visibility set of 
if every pair of vertices in 
is 
-visible (Di Stefano 2022, Tonny and Shikhi 2025).
The maximum cardinality of a mutual-visibility set of 
is called the mutual-visibility
number.
The visibility polynomial records mutual-visibility sets by size: if 
is the number of mutual-visibility sets of 
of size 
, and 
is the mutual-visibility
number, then
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