I wanted to know if the following family of graphs has a name in graph theory: A claw with paths of any length attached to the three free vertices of the claw. More formally, a connected acyclic graph, with 1 vertex of degree 3 and the rest of degree 2 or less.


They're interesting because they arise in the study of graph minors. (In particular, if a graph of this type is a minor of another graph G, then it is also a subgraph of G.)



A name for a claw-graph with paths attached to it
I don't see any reason not to call them "subdivisions of claws," since that's exactly what they are; people working in subfactors [apparently](https://mathoverflow.net/questions/86/a-name-for-star-graph-with-long-laces) call them "star-shaped," or I guess in this case "claw-shaped." I don't know of any other name for them, though.


Now that I think about it, aren't these exactly the trees with exactly three leaves? Do trees with a specified number of leaves have a name?


