Terminal graphs for identifying codes: answers to two questions of Charon, Honkala, Hudry and Lobstein (manuscript, verification code, and exhaustive censuses)

Manuscript and complete verification package for the paper "Terminal graphs for identifying codes: answers to two questions of Charon, Honkala, Hudry and Lobstein". A connected graph is r-twin-free if its closed radius-r balls are pairwise distinct, and r-terminal if deleting any one vertex destroys r-twin-freeness. The paper answers two questions of Charon, Honkala, Hudry and Lobstein (Electron. J. Combin. 14 (2007), R16), repeated as Open Problems 1 and 2 in the 2024 survey of Hudry, Junnila and Lobstein. Main results: (1) the minimum order of a 2-terminal graph other than P5 is nine; there are exactly 99 such graphs, with an explicit hand-checkable outerplanar subcubic example; (2) for every r ≥ 2 and k ≥ 1 the k-th power of the path on 2kr+1 vertices is r-terminal, so infinitely many r-terminal graphs exist for every r ≥ 2, all unit interval; (3) no power of a cycle is ever r-terminal: Cnk is r-twin-free exactly when n ≥ 2kr+2, and every one-vertex-deleted cycle power remains r-twin-free; (4) exhaustive censuses over all connected graphs through order eleven (1,006,700,565 isomorphism classes at order eleven) for radii 2–5: terminal counts 99, 25, 7538 at orders 9–11 for r = 2; 29 at order 11 for r = 3 (all subcubic); only P9 and P11 for r = 4 and r = 5; (5) the conjecture that no r-terminal graph has order in [2r+2, 2r+4]. Contents: the manuscript (paper.tex, paper.pdf), two independently written C scanners with explicit connectivity tests, Python and NetworkX verification scripts, exact witness checkers for both theorems, complete graph6 lists of all positive instances, the connected-graph catalogues through order nine, a per-stream coverage certificate for the order-eleven scans, and a SHA-256 manifest. This record merges, extends, and supersedes the two preliminary notes 10.5281/zenodo.21557862 and 10.5281/zenodo.21569442.