A 24-year-old has been arrested in connection with assault as part of the investigation.
Heartbroken Alex Gibson posted 'rest in peace little angels' after the siblings, aged 12, eight and five, died in hospital.
Eliburn Mini Market in Jackson Place, Livingston, was torched during the early hours of Tuesday.
The blazes have been set in the Sanquhar and Kelloholm areas of Dumfries and Galloway over the past few weeks.
The blaze broke out in Dumfries and Galloway on Thursday, sending the Galloway Hills up in flames.
Emergency services were alerted to the fire in Huntingtower Road, Glasgow, at around 5.30pm on Saturday.
The fire broke out in the Mossdale area on Thursday, sending the Galloway Hills up in flames.
The blaze broke out in forestry near Bannockburn around mid-afternoon on Friday.
The takeaway, on Glasgow Road in Kilmarnock, was targeted at around 1.15am on Friday.
Workers had a narrow escape after a fire broke out in the vehicle.
M & D’s Hair Studio in Kilmarnock was extensively damaged by the blaze on Monday.
Three of the blazes were set on the same night, while a fourth took place six days later.
Emergency services remain at the scene in the centre of Macduff in Aberdeenshire.
Emergency services were alerted to the fire at Garngad Takeaway in Glasgow on Saturday afternoon.
Primary pupils have been left devastated at the destruction of the popular facility.
The two family pets were injured in the 'reckless and cruel' incident in Peterhead on Thursday.