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.
A family of graphs that cannot occur as character degree graphs of solvable groups.Beitr¨ age zur Algebra und Geometrie/Contributions to Algebra and Geometry, 66(3):727– 738
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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.