The problem is that you seem to be aware that

while( <IN> ) {...
[download]

reads a single line, hence you need to loop back to read the next one, but then when you get to

if(/POLY/) {
    $final_gset[$i] = <IN>;
...
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you seem to be expecting that line to somehow magically read multiple lines. It won't.

I might go into a more detailed explanation, but I still think that you don't need to write this program. You are (trying to ) read all the lines from one file and then append them to another. This would be much more easily accomplished using

C:\> type graph_set.txt >>test.txt

or$ cat graph_set.txt >>test.txt

depending which view of the world you see as being rightous:)