The moth graph is the 6-vertex graph illustrated above.
It is implemented in the Wolfram Language as GraphData["MothGraph"].
The Chilakamarri graphs include a different moth graph on 47 vertices.
Moth Graph
See also
Butterfly Graph, Chilakamarri Graphs, Cricket GraphExplore with Wolfram|Alpha
References
House of Graphs. "Moth Graph." https://houseofgraphs.org/graphs/1232.Vijayakumar, A. "Name of a Graph." 27 Mar 2008. https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0803&L=graphnet&P=1566.Referenced on Wolfram|Alpha
Moth GraphCite this as:
Weisstein, Eric W. "Moth Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MothGraph.html