Looks like Acacia baileyana, COOTAMUNDRA WATTLE. Common. Joe

If one assumes it's either baileyana or dealbata, here are descriptions of both that should lead to an ID. I didn't take time to search through the descriptions and compare; I'll leave that to you. Acacia baileyana: http://plantnet.rbgsyd.nsw.gov.au/cgi-bin/NSWfl.pl?page=nswfl&lvl=sp&name=Acacia~baileyana Acacia dealbata: http://plantnet.rbgsyd.nsw.gov.au/cgi-bin/NSWfl.pl?page=nswfl&lvl=sp&name=Acacia~dealbata Here is a link that might be useful: World Wide Wattle

Coral tree -- Erythrina is the genus --not native, they are from South America, I think--there are many many in my OC neighborhood. They get huge and need careful pruning nearly every year because the wood is heavy and weak--many snap in Santa Ana Wind season. Also not clean, they drop a lot of stuff--flowers, twigs, branches, leaves--almost year-round. People who have them around here don't like them much, but they quickly get too big (70') and thus too expensive to remove. Until they fall over. But it gets windy here. Exactly how much space do you have? For many Orange County yards, a large shrub works far better than a "tree". A large shrub can be 20' tall and provide plenty of shade, while a small tree can be 35' and grow to large for the small lot that many Orange County houses are built on. Look at Agonis flexuosa. There is a green version and a version with very dark purple foliage called 'After Dark'. Clean, drops little litter, deep, non-invasive root system, gives good shade but does not get huge, drought tolerant once established. Not native, though. Pittosporum 'Silver Sheen', lovely with a silvery shine to the leaves in sunlight, grows fast, doesn't get huge. Also not native. The native oaks are beautiful but they have aggressive and invasive roots, eventually. The native Sycamore is simply to large for most properties. Cercis are okay, but rather mess. Catalina Ironwood, maybe. Some of the Manzanitas are lovely. A really good idea would be to walk around your neighborhood and see what looks good and what you like and what would be an appropriate size. Right away you know it will grow well at your house if it is already growing well in the neighborhood. You can take a picture and post it for identification if you don't know what it is, or ask at your local garden center. If there are power lines in the area, please don't plant a tree that will get very large that will end up like this:

Hello, Is the Eucalyptus plant outside or do you have it inside a heated area? If you have it outside, it could be the cold weather that is killing it. Ohio is a bit cold for most eucalyptus trees from what I can remember (although I think there are a few species that will grow in your USDA growing zones). If it's indoors, then I'm having the same problem with mine (gangly growth, and it's dying back, but I think the dying back might be due to a nutrient deficiency in my soil) I'm thinking that the gangly growth could be due to the higher indoor temperatures combined with low light levels of winter, although I could be wrong there. Hope that helps and Good luck with your plant :) -Adam PS: I know that there's an invasive eucalyptus problem in California because of the similar Mediterranean-style climate to many parts of Australia. Considering the big difference in climate between Ohio and Australia, I wouldn't think there'd be any problem with eucalyptus becoming invasive there.