Ian
I've been going round in circles for a while with Alexander

I've had a look at this death cert in 1933 and I think mother may have been a Janet McLellan (has lots of variants although not McKillan which I now think just the way it may have been written up.
We have the marriage of an Andrew Graham and a Janet McLellan in 1879 in Douglas Lanark. You mentioned Douglas earlier in your post regarding Alexander.
This looks to be Janet's birth details on IGI:
JANET MUIR MCLELLAN Birth:18 MAY 1855 Douglas, Lanark
Parents:JOHN MCLELLAN and MARY CLARKSON
And for Andrew Graham, an illegitimate birth:
ANDREW GRAHAM Birth: 01 DEC 1856 Lesmahagow, Lanark
Parents: MARY GRAHAM
These details match what is on the marriage cert.
Census info for this family:
Andrew Graham 34, Ploughman Agr Labourer, b. Lesmahagow
Janet Graham 34, b. Douglas
Mary Graham 11, b. Lesmahagow
Margaret Graham 9, b. Douglas
Grace Graham 8, b. Douglas
Andrew Graham 6, b. Douglas
John Graham 5, b. Douglas
Hugh Graham 3, b. Douglas
Agnes Graham 1, b. Lesmahagow
William Graham 11 Days, b. Crawfordjohn
Address:Nether Abington Cottage, Crawfordjohn, Lanarkshire
And in 1901:
Andrew Graham 45, Ag Lab Ploughman
Grace Graham 18
Andrew Graham 16
John Graham 15
Hugh Graham 13
Agnes Graham 11
William Graham 10
Alexander Graham 7, b. Cranfordjohn, Lanarkshire
Address: Braehead, Cramond Midlothian
There is a death showing in 1900 in Cramond for a Janet Graham/M*c*le*
Why don't you contact the Strathclyde Police Archives at
www.strathclyde.police.uk/index.asp?locID=448&docID=-1 to see whether you can find his record (which may well include his place of birth and personal details from some other I have seen).
Monica