Consider a star graph 
consisting of a central hub vertex and 
spokes, but instead of placing a single point at the end of
each spoke, place 
points along it (in addition to the shared central point). While this graph has been
considered by various authors, it apparently has not been given a standard name.
In this work, to avoid confusion with star graphs and permutation
star graphs, the term 
spoke graph is used.
Spoke Graph
See also
Helm Graph, Star Graph, Web Graph, Wheel GraphExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Spoke Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpokeGraph.html