Can you boil vegetables along with eggs? When boiling eggs if you also want to boil vegetables it might be more efficient to boil them with the eggs rather then use more water and another pan.
Is it safe to do this or should one boil the vegetables in another pot?
Yes, you can do this. Be aware that:

if you add lots of cool items to boiling water it will take longer to start boiling again, which may impact cooking time a little.
I can imagine vegetables with very strong colour (beetroot) or flavour (garlic?) might diffuse through the eggshell and give you a pink or slightly garlicky egg.