Detective Senior Sergeant Stephen McIntyre said police had not made any arrests.
"We're ... trying to identify motives, but it's early days," he told the Herald Sun.
"We're trying to track any movements to and from the address."
Neighbours described the home as the scene of frequent arguments.
Sheila O'Brien said she had been good friends with Ms Parker since she moved into the Ministry of Housing units "many years ago".
"She always stopped and talked to me and asked me how I was. It was a dreadful, dreadful shock. She was really lovely and will be missed a lot."
Ms O'Brien said she hadn't slept since she heard the news about Ms Parker's death and it had been a "bad day" for the neighbourhood.
Ms Parker worked as a cleaner at the nearby Dandenong Plaza. A cat and a cockatiel in Ms Parker's house were put into the care of a friend.
Nicole Tiley described Ms Parker as an "amazing friend and mother".
"Still doesn't feel real ... who could of done that to such a beautiful and caring person ... you are gonna be missed so much," she wrote on Facebook.
She told Ms Sweet to keep her head up. "... remember your mum will be looking down on you and she would be proud."