Both victims were discovered at 8:45am on Thursday morning.
A Home Office post-mortem examination on Dr Sacharvi showed on Saturday that she died from pressure to her neck and that she was also assaulted before she died.
Tests have shown Vian was badly burnt, but officials have not yet determined the cause of her death.
Officers who attended the house on Colne Road, Burnley, discovered their bodies along with evidence of fire and smoke inside.
Their next of kin have been informed and they are being supported by specially trained officers.
Vian was a pupil at Marsden Heights School in nearby Nelson.
Lancashire Police urged anybody with information about their deaths to make contact with them as soon as possible.
Detective Superintendent Jon Holmes, head of major crime, said they have a number of lines of inquiry and have made two arrests.
He said: “However this is a live investigation and we continue to ask anyone with any information to get in touch with us.
“Perhaps you have been in the Colne Road area recently and have seen something suspicious.
“Maybe you have CCTV or dashcam footage which could contain something useful. Or perhaps you think you know who is responsible.
“Whatever information you have, we would urge you to get in touch, even if you think what you know is insignificant.
“We have a team of detectives dedicated to the investigation and we will leave no stone unturned.”
Both men remain in police custody.
Anyone with information can contact police quoting log 0298 of October 1, or independent charity Crimestoppers on 0800 555 111.