{"id":"hexagon/2610.00318","pdf":"https://hexagonmath.org/pdf/2610.00318v1","url":"https://hexagonmath.org/abs/2610.00318v1","tags":["math.GR","msc:05C60","msc:05C25","msc:20D15","msc:68V15","Cayley graph","Suzuki 2-group","divisible design graph","pseudosimilar vertices","vertex-deleted subgraph"],"score":0,"title":"A graph with three card types and five vertex orbits","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee","Ushashi Bhattacharya"],"reviews":0,"subject":"math.CO","summary":"We prove that the answer to part~(b) of Problem~20.71 of the Kourovka Notebook is yes: there is a connected graph on $63$ vertices with exactly three isomorphism types of vertex-deleted subgraphs whose automorphism group has five orbits on the vertices. The graph is a Cayley graph of a Suzuki $2$-group of order $64$ with one vertex removed.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-17","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}