The late Poul Anderson was always one of my favourite sf writers, and this is an absolutely vintage specimen.
Human explorers come back to find the Earth destroyed, and badly need to find out whodunit, if only to assure that the killers aren't also a danger tot hem. While doing so, they also have to find ways to go on living in a not particularly human-friendly galaxy. It's beautifully done, the alien races are well drawn as only Anderson could, and problem is ingeniously solved.
Perhaps one very minor gripe. I always preferred the title used for the magazine version in Galaxy - "The Day After Doomsday". Somehow the shorter title loses some of the oomph - but it's not important. Don't miss it.