Jack Lis, 10, was mauled to death at the home of a friend in Pentwyn, Penyrheol, on Monday. Gwent Police launched an investigation and on Wednesday confirmed they had arrested a woman on suspicion of being in charge of a dog dangerously out of control causing injury resulting in death. She has been released conditional bail, the force said.
Chief Superintendent Mark Hobrough said work was continuing to identify the breed of the dog, which people locally have claimed was a type of American pit bull.
People commenting on social media have been warned to consider their language before posting while an active investigation is ongoing.
Mr Hobrough said: "As we've arrested an individual on suspicion of an offence linked to the attack, and spoken to two others voluntarily, we're looking to identify where any criminal matters have occurred.
"I understand that there is a lot of interest about this in our communities.
"It is vital that people are considering the tone and language used in comment posted on social media about the identities of anyone involved in this matter as part of our enquiries.
"As this is a live investigation such comments may have impact on our ability to bring anyone found to have committed a criminal offence to justice."
Anyone with information is asked to call the police on 101, quoting log reference 2100392510.
You can also send a direct message on Facebook or Twitter. Alternatively, you can contact Crimestoppers anonymously by calling 0800 555 111.
The two men who have since been released were a 34-year-old from the Mountain Ash area and a 19-year-old from the Caerphilly area.
Jack and his friend had been alone at the time of the incident.
After the dog attacked Jack, his friend sought the help of a neighbour but they were unable to stop the animal.
Paramedics arrived at the scene just before 4pm but were unable to save Jack.
The animal was shot by officers at the scene.
Speaking on Monday, local councillor Steve Skiven expressed his sadness over the death of the young boy.
He told Wales Online: "Our thoughts go out to the family and friends of the young man who has lost his life.
"We would also like to extend our thoughts to all the emergency services who attended the incident.
"Unfortunately an animal had to be put down.
"We await the details from the police.
"It's a tragic, tragic loss of a young life."
Locals also expressed their sadness, with one describing Jack as a "lovely boy".