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They capture crucial features of the reaction mechanism and thus play a central role in modeling chemistry at the level of graph transformations. AAMs are equivalent to so-called \u201cimaginary transition state\u201d (ITS) graphs, making it possible to reduce tasks such as the computational comparison of AAMs to testing graph isomorphisms. In many application scenarios, nonetheless, only partial information is available, i.e., only partial maps or, equivalently, only subgraphs of the ITS graphs, are known. Here, we investigate whether and how, and to what extent, such partial chemical data can be completed and compared. The focus of this contribution is entirely on the development of a solid mathematical foundation for the analysis of partial AAMs and their associated partial ITS graphs.<\/jats:p>","DOI":"10.3390\/sym16091217","type":"journal-article","created":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T07:36:00Z","timestamp":1726472160000},"page":"1217","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Partial Imaginary Transition State (ITS) Graphs: A Formal Framework for Research and Analysis of Atom-to-Atom Maps of Unbalanced Chemical Reactions and Their Completions"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-2307-595X","authenticated-orcid":false,"given":"Marcos E.","family":"Gonz\u00e1lez Laffitte","sequence":"first","affiliation":[{"name":"Bioinformatics Group, Department of Computer Science & Interdisciplinary Center for Bioinformatics, Leipzig University, H\u00e4rtelstra\u00dfe 16-18, D-04107 Leipzig, Germany"},{"name":"Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Leipzig University, D-04103 Leipzig, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3349-9157","authenticated-orcid":false,"given":"Klaus","family":"Weinbauer","sequence":"additional","affiliation":[{"name":"Bioinformatics Group, Department of Computer Science & Interdisciplinary Center for Bioinformatics, Leipzig University, H\u00e4rtelstra\u00dfe 16-18, D-04107 Leipzig, Germany"},{"name":"Machine Learning Research Unit, TU Wien Informatics, Erzherzog-Johann-Platz 1 (FB02), A-1040 Wien, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3532-2064","authenticated-orcid":false,"given":"Tieu-Long","family":"Phan","sequence":"additional","affiliation":[{"name":"Bioinformatics Group, Department of Computer Science & Interdisciplinary Center for Bioinformatics, Leipzig University, H\u00e4rtelstra\u00dfe 16-18, D-04107 Leipzig, Germany"},{"name":"Department of Mathematics and Computer Science University of Southern Denmark DK-5230 Odense, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-0548-3485","authenticated-orcid":false,"given":"Nora","family":"Beier","sequence":"additional","affiliation":[{"name":"Bioinformatics Group, Department of Computer Science & Interdisciplinary Center for Bioinformatics, Leipzig University, H\u00e4rtelstra\u00dfe 16-18, D-04107 Leipzig, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0748-0630","authenticated-orcid":false,"given":"Nico","family":"Domschke","sequence":"additional","affiliation":[{"name":"Bioinformatics Group, Department of Computer Science & Interdisciplinary Center for Bioinformatics, Leipzig University, H\u00e4rtelstra\u00dfe 16-18, D-04107 Leipzig, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5500-2415","authenticated-orcid":false,"given":"Christoph","family":"Flamm","sequence":"additional","affiliation":[{"name":"Department of Theoretical Chemistry, University of Vienna, W\u00e4hringerstra\u00dfe 17, A-1090 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5567-3016","authenticated-orcid":false,"given":"Thomas","family":"Gatter","sequence":"additional","affiliation":[{"name":"Bioinformatics Group, Department of Computer Science & Interdisciplinary Center for Bioinformatics, Leipzig University, H\u00e4rtelstra\u00dfe 16-18, D-04107 Leipzig, Germany"},{"name":"Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Leipzig University, D-04103 Leipzig, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7792-375X","authenticated-orcid":false,"given":"Daniel","family":"Merkle","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science University of Southern Denmark DK-5230 Odense, Denmark"},{"name":"Algorithmic Cheminformatics Group, Faculty of Technology, Bielefeld University, 33615 Bielefeld, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5016-5191","authenticated-orcid":false,"given":"Peter F.","family":"Stadler","sequence":"additional","affiliation":[{"name":"Bioinformatics Group, Department of Computer Science & Interdisciplinary Center for Bioinformatics, Leipzig University, H\u00e4rtelstra\u00dfe 16-18, D-04107 Leipzig, Germany"},{"name":"Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Leipzig University, D-04103 Leipzig, Germany"},{"name":"Department of Theoretical Chemistry, University of Vienna, W\u00e4hringerstra\u00dfe 17, A-1090 Vienna, Austria"},{"name":"Max Planck Institute for Mathematics in the Sciences, Inselstra\u00dfe 22, D-04103 Leipzig, Germany"},{"name":"Center for Non-Coding RNA in Technology and Health, University of Copenhagen, DK-1870 Fredriksberg, Denmark"},{"name":"Facultad de Ciencias, Universidad Nacional de Colombia, Sede Bogot\u00e1, Bogot\u00e1 CO-111321, Colombia"},{"name":"Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM 87501, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,16]]},"reference":[{"key":"ref_1","unstructured":"(2024, July 20). 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