Because eucalyptus forests are sometimes shrouded in a smog-like mist of vaporised volatile organic compounds (terpenoids); the Australian Blue Mountains take their name from the haze. I've been there and it's true!

Please have a look at this link.

https://en.wikipedia.org/wiki/Eucalyptus

Another hypothesis refers to the stem of the tree that remembers a bullet ("gum")

http://www.hornsby.nsw.gov.au/media/documents/environment-and-waste/bushland-and-biodiversity/native-tree-database-fact-sheets/Fact-sheet-Eucalyptus-saligna-Sydney-Blue-Gum.pdf

http://www.cal-ipc.org/ip/management/wwh/pdf/19654.pdf

More details can be found in the following link and may they help;

 https://en.wikipedia.org/wiki/Eucalyptus_globulus

If you see the yang tree of Eucalyptus deglupta Bl. it has green tronc, later - blau, and after - all color of Rainbow

see also:

David Webster Lee. Nature's palette: the science of plant color. — University of Chicago Press, 2007.

Blue gum is a common name for subspecies or the species in Eucalyptus globulus complex, and also a number of other species of Eucalyptus in Australia. Confusingly, in Queensland it usually refers to Eucalyptus tereticornis, which is known elsewhere as forest red gum.

https://en.wikipedia.org/wiki/Blue_gum

Eucalyptus saligna, known as the Sydney blue gum, is a large Australian hardwood (flowering) tree common along the New South Wales seaboard and into Queensland, which can reach a maximum of 65 metres (213 feet) in height.It is a common plantation timber in Australia and South Africa.

https://en.wikipedia.org/wiki/Eucalyptus_saligna

Many eucalypts are called "gum trees" because of a sticky, gum-like substance they exude from their trunks.