The forward duo were both in action for the Hoops' second string this week as the Parkhead kids beat Partick Thistle in an Under-20 fixture.
While Griffiths was only on show for the first 45 minutes at Lennoxtown as he made his debut in green and white following his deadline-day switch from Wolves, his Icelandic strike partner marked his second full game with a goal in a comfortable 4-0 win.
And Fridjonsson is determined to catch the eye of boss Neil Lennon and force his way into top-team reckoning at Parkhead. The 20-year-old said: "It feels really good to score my first goal for the club. As a striker, scoring is what you are here to do and it comes with a bit of relief.
"I saw John Herron had the ball at the corner of the box and I made the decision to attack the back post and it was a good pass from him which made it easier for me.
"I also enjoyed linking up with Leigh. He only got 45 minutes, but you could see that he is a really good player.
"I think he is the sort of player I'd enjoy playing with on a regular basis because if you have two big players up front, sometimes it doesn't work, so the combination with myself and someone with pace works really well.
"My fitness is getting better and better. I still feel myself tiring a little bit in games, but off the field I'm working hard and I'm trying to run as much as I can and getting as much extra work as I can.
"Hopefully, I can impress the manager soon and get my chance."
While Fridjonsson may have to play the waiting game before being handed his first-team bow, Griffiths is in line to make his Hoops debut when Celtic face Aberdeen on Scottish Cup duty on Saturday.
The champions will clinch their third successive top-flight crown in a matter of weeks, and defender Efe Ambrose is determined to keep up the momentum as they bid to extend their superb unbeaten run.
"We know Aberdeen are a good team and are in good form, but this is Celtic we are talking about - we are here to do something new and perform at a level no-one believes we can play at," he told the Celtic View.
"So we will keep doing what we are doing, keep winning games and keep doing the defensive part of the game right, and we will see where it takes us."