New home with Eucalyptus tree

[marlei]

My husband and I have just bought a log home in SC. It has a eucalyptus tree near the front porch. I'm not sure what type. It has the leaves like you see in stores, and is used in wreaths and decorations. This is new to me and I'm not sure when we need to prune it, or if you do. There is a section in the middle that has some leaves turning brown. What do I do?
Thank you

 

[Ekka]

My husband and I have just bought a log home in SC. It has a eucalyptus tree near the front porch. I'm not sure what type. It has the leaves like you see in stores, and is used in wreaths and decorations. This is new to me and I'm not sure when we need to prune it, or if you do. There is a section in the middle that has some leaves turning brown. What do I do?
Thank you

You post some pictures so we can have a look, there's over 800 of the buggers.

Make sure pictures are both full tree shots as well as close ups.