The problem with wiring leds in parallel with just one series current limiting resistor, is that if they have even a slight difference in Vf (forward voltage drop, which they will) then one will turn on before the other, robbing all or most of the current. So because you can't guarantee equal current sharing between the leds you should not wire them in parallel unless each has it's own series current limiting resistor.
And if you are playing around with wiring your leds to a 9vdc battery or to a arduino output pin without using current limiting resistors (you didn't state one way or another) you are in danger of damaging the leds and/or arduino output pins.
Lefty