A chemical graph with Mostar index 5

A chemical graph with Mostar index 5 The Mostar index of a connected graph is the sum over its edges uv of |n_u - n_v|, where n_u counts the vertices closer to u than to v. A chemical graph is a connected graph with maximum degree at most 4. Alizadeh, Bašić, Damnjanović, Došlić, Pisanski, Stevanović and Xu (Solving the Mostar index inverse problem, J. Math. Chem. 62(5) (2024) 1079-1093; arXiv:2312.13083) report that every graph they found with Mostar index 5 has maximum degree 5, write that a chemical realisation of 5 seems unlikely, and ask in Problem 9 whether 5 is the only integer greater than one that no chemical graph realises. This record gives two non-isomorphic connected graphs on 13 vertices and 22 edges, with degrees 3^8 4^5, whose Mostar index is 5 (graph6: L?Oc]?PMAHAKk@ and LEHA?oBi@Gdc_a). The paper shows that every integer other than 1, 3 and 5 is the Mostar index of a chemical graph, and that 3 is too. With these graphs, every nonnegative integer other than 1 is the Mostar index of a chemical graph, which answers Problem 9. Contents: the graphs (graph6 and edge lists), a standard-library Python verifier with controls and a planted-error test and its output, a second checker written from the definitions and its output, a results table, and a README with the quoted statements, method, prior-work search and limits. Whether a 12-vertex example exists is open. Searches and verification were carried out with Claude (Anthropic) under the direction of Kerem Özdemir.