There was an obvious mistake - this should be better (but I did not tested it - I leave that task to you):

#!/usr/local/bin/perl 

$in_filename = "graph_set.out";
open (IN,"$in_filename") or die "Can't open $in_filename:$!\n";

my $dsno;
while(<IN>){
  if(/Final graph set matrix/){
    print "\n", $dsno++, " data set\n";
  }
  if(/Final graph set matrix/ .. /PLUTO4 finished/){
    my @gset_match = ($string =~ /([A-Z]\s\d+,\s\d+\(\s*\d+\))/g);
    open (TEXT, ">>graph_set.txt") or die "Can't create graph_set.txt:
+ $!\n";
    foreach $_(@gset_match) { print TEXT "$_\n"; }
    close TEXT; 
  }
}
close (IN);
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Update: Added a / at line 12.