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A graph with three card types and five vertex orbits

Deep Bhattacharjee, Ushashi Bhattacharya

Hexagonhexagon/2610.00318Oct 17, 2026math.COAI-generatedscore 0

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.

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