GraphTheory-VL: Visual Instances for Exact Mathematical Reasoning

A mathematical drawing specifies an instance, while a solution must recover that instance and compute its requested target. A final answer alone can hide an incorrect structural interpretation, and removing the drawing can make a reasonable refusal indistinguishable from a failed solution. We introduce GraphTheory-VL, a collection of 62 visual mathematics problems with an embedded 20-problem hard subset, linking graph, algebraic, and topological targets to reference checks and complete model responses. We evaluate three model families with four responses per problem and compare original-image and text-only inputs on the hard subset. Mean accuracy on the 62-problem collection ranges from 10.89% to 31.85%, while the hard subset remains at 1.25% to 5.00%. Across models, at least one response succeeds on 43 of 62 problems, but only five of the 20 hard problems. An analysis of all 120 first responses in the image ablation distinguishes reasonable uncertainty, unsupported instance assumptions, and observable mathematical errors. In particular, a text-only response can match the target after guessing an omitted parameter, whereas a response that correctly identifies a graph can still compute the wrong critical group. These results connect repeated correctness to the mathematical and visual evidence needed to interpret it.