Classification of Strongly Prime Smooth Graphs

Definitions and mathematical statement

The supplied record asks for a characterization and classification of the strongly prime smooth graphs. It does not define either smooth or strongly prime, and it does not specify the ambient class of graphs.

Let $\mathcal G$ denote the intended ambient graph class, which remains unspecified. Using the terminology of the cited report, the requested class is schematically \[ \mathcal C=\{G\in\mathcal G: G\text{ is smooth and strongly prime}\}. \] The problem is to characterize and classify $\mathcal C$. This formulation records the intended target only: the definitions of both properties, the graph conventions, and the intended equivalence relation for classification must be recovered from the source before a fully specified mathematical statement can be given. In particular, no restriction to finite, simple, connected, or undirected graphs is imposed here without source evidence.

The supplied record labels this problem open and reports that the source calls its identification an interesting open problem. Its dated assessment also states that cited results classify broad smooth subclasses but do not classify the strongly prime smooth graphs; the record supplies neither those results nor their precise hypotheses. These are supplied source qualifications, not independently verified mathematical or literature conclusions.

Short English statement

Identify and classify the graphs that are both smooth and strongly prime in the terminology of the cited report. The supplied record omits the definitions and graph conventions needed to make this classification problem precise.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30006608$, title: Classification of Strongly Prime Smooth Graphs; exact source problem code: catalogue entry. No individual proposer is identified; the supplied proposed year is 2026.
• Median Geometry and Applications (2026), Oberwolfach Reports, pp. 487--540, DOI 10.4171/owr/2026/8. Supplied source citation and literature-source label: Oberwolfach Report 8/2026. https://doi.org/10.4171/owr/2026/8. The record attributes the problem to workshop open-problem discussions documented in this report; it does not identify the precise passage or speaker.
• Literature assessment dated 2026-08-22: the supplied curation labels the problem open and states that broad smooth subclasses have been classified, whereas identification of the strongly prime smooth graphs remains open. This is supplied dated curation, not independently verified; its time-sensitive status and cited claims require independent checking.