History
Cacti were first studied under the name of Husimi trees, bestowed on them by Frank Harary and George Eugene Uhlenbeck in honor of previous work on these graphs by Kodi Husimi. The same Harary–Uhlenbeck paper reserves the name "cactus" for graphs of this type in which every cycle is a triangle, but now allowing cycles of all lengths is standard.
Meanwhile, the name Husimi tree commonly came to refer to graphs in which every block is a complete graph (equivalently, the intersection graphs of the blocks in some other graph). This usage had little to do with the work of Husimi, and the more pertinent term block graph is now used for this family.
Read more about this topic: Cactus Graph
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