Sarabjit Kaur, 38, was found dead in her house by her husband and step children when they returned from school.
It is believed that she was attacked and killed a few hours before her body was found.
Police released her picture today and appealed to anyone with information to come forward.
Extra officers have been assigned to the case to complete the investigation quickly.
The Rookery Lane house in Wolverhampton remains sealed as forensic department is looking for any evidence that could help in identifying the murderer.
The cause of her death could not be revealed from a post mortem examination.
Det Chief Insp Chris Mallett, from the force’s homicide team, said: “Mrs Kaur was attacked in her own home: this is a shocking and thankfully rare case.
“We are determined to bring her killer or killers to justice.
“Forensics experts are methodically picking through items inside the house that could be of evidential value and we will be fast-tracking forensic samples for analysis.
“We are building up a clearer CCTV picture in the immediate vicinity of the crime scene and are drafting in additional officers to help with the CCTV trawl and examination of footage.
“We found the interior of the property in an untidy state − which could indicate it had been searched − and we believe some jewellery items are missing.
“We are working with the family to understand exactly what items may have been taken.
“However, the motive is unclear; we are keeping an open mind and examining several lines of enquiry.
“I would urge anyone who saw anything suspicious in the Rookery Lane area last Friday, no matter how insignificant it may seem, to contact us.”
There have been around 150 burglaries in Wolverhampton so far this year but Det Chief Insp Mallett said none involved occupants being subjected to serious violence.
He added: “We are re-examining many of these burglaries and expediting investigative opportunities to establish if there could be any link with Mrs Kaur’s death. However, we have not seen any home invasion offences recently in Wolverhampton where extreme levels of violence have been used.
“We have conducted house-to-house enquiries and police officers have been out and about on patrols in the local area, speaking to members of the public and offering reassurance.
“We would always urge residents to be vigilant, to report any suspicious activity, and to take common sense crime prevention measures like keeping doors and windows locked and not to let any unsolicited callers into your home.”
Anyone with information should call the homicide team on 101 or Crimestoppers, in confidence, on 0800 555 111.