The police are reassuring parents that rumours circulating on social media about suspects putting children at risk are unfounded.
One mother reported to the police that she believed that her 13-year-old daughter had been followed on her way home from school by a man in Bearsden on Friday, May 8.
She also posted a warning on facebook to other parents which included details of other sightings of men allegedly acting suspiciously including in the Kessington area of Bearsden near the medical centre and within the grounds of Douglas Academy in Milngavie.
However the police are satisfied that there is no evidence that any of these men were behaving in a suspicious way.
Inspector Gerry Corrigan of Kirkintilloch Police Office, said: “The girl seems to have got a bit of a fright when a man was walking the same route as her.
“However he did not do or say anything which was in any way threatening.
“His behaviour does not appear to have been worrying but nevertheless we have taken this report seriously and carried out extensive enquiries to satisfy ourselves there is nothing untoward.
“We always take reports of suspicious behaviour seriously and investigate fully.
“We have attended and spoken to the deputy headteacher at Douglas Academy in Milngavie, about reports of a man seen in the grounds watching the girls play hockey.
“He and the police are satisfied that this is untrue and there was nothing suspicious, it was simply a man walking along the public footpath.
“Schools as a matter of course get extra police attention by our community police officers and will continue to do so.
“The incident on the 8 May appears to be a one off and there’s no evidence at the moment that there was any malice in it.
“While we understand that parents are concerned, we’d encourage people not to spread rumours which could cause alarm on social media but rather report all instances of suspicious behaviour to the police.”
If you have any information about anyone acting in a suspicious way call the non-emergency phone number 101.