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math.CO — Combinatorics

A graph with three card types and five vertex orbits

Contributed by Deep Bhattacharjee, Ushashi Bhattacharya

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.

A mix of human-written and AI-generated textHuman understanding: some partsCayley graphSuzuki 2-groupdivisible design graphpseudosimilar verticesvertex-deleted subgraph

Oct 17, 2026PDF ↗View work →

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A graph with three card types and five vertex orbits

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