{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T11:09:26Z","timestamp":1762254566689,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,9]],"date-time":"2023-07-09T00:00:00Z","timestamp":1688860800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009391","name":"Deanship of Scientific Research at University of Tabuk","doi-asserted-by":"publisher","award":["S-0140-1443"],"award-info":[{"award-number":["S-0140-1443"]}],"id":[{"id":"10.13039\/100009391","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The inverse in crisp graph theory is a well-known topic. However, the inverse concept for fuzzy graphs has recently been created, and its numerous characteristics are being examined. Each node and edge in m-polar fuzzy graphs (mPFG) include m components, which are interlinked through a minimum relationship. However, if one wants to maximize the relationship between nodes and edges, then the m-polar fuzzy graph concept is inappropriate. Considering everything we wish to obtain here, we present an inverse graph under an m-polar fuzzy environment. An inverse mPFG is one in which each component\u2019s membership value (MV) is greater than or equal to that of each component of the incidence nodes. This is in contrast to an mPFG, where each component\u2019s MV is less than or equal to the MV of each component\u2019s incidence nodes. An inverse mPFG\u2019s characteristics and some of its isomorphic features are introduced. The \u03b1-cut concept is also studied here. Here, we also define the composition and decomposition of an inverse mPFG uniquely with a proper explanation. The connectivity concept, that is, the strength of connectedness, cut nodes, bridges, etc., is also developed on an inverse mPF environment, and some of the properties of this concept are also discussed in detail. Lastly, a real-life application based on the robotics manufacturing allocation problem is solved with the help of an inverse mPFG.<\/jats:p>","DOI":"10.3390\/sym15071387","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T00:45:37Z","timestamp":1688949937000},"page":"1387","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Inverse Graphs in m-Polar Fuzzy Environments and Their Application in Robotics Manufacturing Allocation Problems with New Techniques of Resolvability"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7909-2539","authenticated-orcid":false,"given":"Abdulaziz Mohammed","family":"Alanazi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5596-5841","authenticated-orcid":false,"given":"Ghulam","family":"Muhiuddin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2404-1555","authenticated-orcid":false,"given":"Tanmoy","family":"Mahapatra","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721 102, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1172-885X","authenticated-orcid":false,"given":"Zaid","family":"Bassfar","sequence":"additional","affiliation":[{"name":"Department of Information Technology, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6709-836X","authenticated-orcid":false,"given":"Madhumangal","family":"Pal","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721 102, India"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,9]]},"reference":[{"key":"ref_1","unstructured":"Rosenfeld, A. (1975). Fuzzy Graphs, Fuzzy Sets and Their Application, Academic Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_3","unstructured":"Zhang, R.W. 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Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s40314-022-01987-z","article-title":"Competition graphs under interval-valued m-polar fuzzy environment and its application","volume":"41","author":"Mahapatra","year":"2022","journal-title":"Comput. Appl. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1597","DOI":"10.1080\/09720529.2015.1117221","article-title":"m-polar fuzzy graphs and m-polar fuzzy line graphs","volume":"20","author":"Akram","year":"2017","journal-title":"J. Discret. Math. Sci. Cryptogr."},{"key":"ref_20","first-page":"27","article-title":"Certain types of edge m-polar fuzzy graph","volume":"14","author":"Akram","year":"2016","journal-title":"IRanian J. Fuzzy Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Akram, M. (2019). m-Polar Fuzzy Graphs, Theory, Methods, Application, Springer International Publishing.","DOI":"10.1007\/978-3-030-03751-2"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/7\/1387\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:09:25Z","timestamp":1760126965000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/7\/1387"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,9]]},"references-count":21,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["sym15071387"],"URL":"https:\/\/doi.org\/10.3390\/sym15071387","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,7,9]]}}}