The "hammer graph" is a name sometimes given to the 
-tadpole graph = 
-lollipop
graph. It is illustrated above in a number of embeddings.
It is the graph complement of the banner graph.
Hammer Graph
See also
Lollipop Graph, Paw Graph, Tadpole GraphExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Hammer Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HammerGraph.html