The gem graph is the fan graph 
illustrated above.
It is implemented in the Wolfram Language as GraphData["GemGraph"].
Gem Graph
See also
Fan GraphExplore with Wolfram|Alpha
References
Brandstädt, A.; Le, V. B.; and Spinrad, J. P. Graph Classes: A Survey. Philadelphia, PA: SIAM, p. 18, 1987.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. "Gem Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GemGraph.html