The banner graph is the 
-tadpole graph illustrated above. It could perhaps also
be termed the 'P graph.'
It is implemented in the Wolfram Language as GraphData["BannerGraph"].
Banner Graph
See also
Tadpole GraphExplore with Wolfram|Alpha
References
ISGCI: Information System on Graph Class Inclusions v2.0. "List of Small Graphs." http://www.graphclasses.org/smallgraphs.html.Cite this as:
Weisstein, Eric W. "Banner Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BannerGraph.html