37 connected eight-vertex prime character degree graphs occur for finite solvable groups (34 via direct products, 3 with diameter three), 56 do not occur, and 206 remain unclassified.
The diameter of the character degree graph..Journal f¨ ur die reine und angewandte Mathematik (Crelles Journal), 1989(402):181–198
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Classifying Prime Character Degree Graphs With Eight Vertices
37 connected eight-vertex prime character degree graphs occur for finite solvable groups (34 via direct products, 3 with diameter three), 56 do not occur, and 206 remain unclassified.