3-6 Graph on 18 Vertices
For my honors thesis, I am studying cubic graphs by concentrating on the construction of cubic cages with large girth. As an introduction to the subject, one of my first tasks was to draw the known cubic cages with girths 3-8. My attempts to draw a cubic graph with girth 6 brought me to this graph construction on 18 vertices.
After discussion with my thesis adviser, I learned my drawing was not a cage, since a graph has been drawn on 14 vertices instead of 18. My next step is to attempt to draw a 3-6 cage on 14 vertices.