{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T00:48:22Z","timestamp":1771462102812,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T00:00:00Z","timestamp":1725321600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T00:00:00Z","timestamp":1725321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Comput Intell Syst"],"DOI":"10.1007\/s44196-024-00626-1","type":"journal-article","created":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T17:02:49Z","timestamp":1725901369000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Fuzzy Outerplanar Graphs and Its Applications"],"prefix":"10.1007","volume":"17","author":[{"given":"Deivanai","family":"Jaisankar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sujatha","family":"Ramalingam","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nagarajan","family":"Deivanayagampillai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7524-7567","authenticated-orcid":false,"given":"Tadesse","family":"Walelign","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,9,3]]},"reference":[{"key":"626_CR1","doi-asserted-by":"crossref","unstructured":"Rosenfeld, A.: Fuzzy graphs, fuzzy sets and their applications to cognitive and decision processes. In: Proceedings of the US\u2013Japan Seminar on Fuzzy Sets and their Applications, Academic Press, pp. 77\u201395 (1975)","DOI":"10.1016\/B978-0-12-775260-0.50008-6"},{"issue":"1","key":"626_CR2","first-page":"145","volume":"22","author":"AN Gani","year":"2003","unstructured":"Gani, A.N., Ahamed, M.B.: Order and size in fuzzy graphs. Bull. Pure Appl. Sci. 22(1), 145\u2013148 (2003)","journal-title":"Bull. Pure Appl. Sci."},{"issue":"4","key":"626_CR3","first-page":"387","volume":"5","author":"F Harary","year":"1959","unstructured":"Harary, F.: Graph theoretic methods in the management sciences. Manag. Sci.. Sci. 5(4), 387\u2013403 (1959)","journal-title":"Manag. Sci.. Sci."},{"issue":"4","key":"626_CR4","first-page":"433","volume":"3","author":"G Chartrand","year":"1967","unstructured":"Chartrand, G., Harary, F.: Planar permutation graphs. Annales de l\u2019institut Henri Poincar\u00e9. Section B. Calcul des probabilit\u00e9s et statistiques 3(4), 433\u2013438 (1967)","journal-title":"Annales de l'institut Henri Poincar\u00e9. Section B. Calcul des probabilit\u00e9s et statistiques"},{"issue":"3","key":"626_CR5","doi-asserted-by":"publisher","first-page":"2619","DOI":"10.3233\/JIFS-213189","volume":"43","author":"G Balaraman","year":"2022","unstructured":"Balaraman, G., Sundareswaran, R., Pal, M.: Strong domination integrity in graphs and fuzzy graphs. Intell. Fuzzy Syst. 43(3), 2619\u20132632 (2022)","journal-title":"Intell. Fuzzy Syst."},{"issue":"3","key":"626_CR6","doi-asserted-by":"publisher","first-page":"2043","DOI":"10.3233\/JIFS-16433","volume":"31","author":"G Ghorai","year":"2016","unstructured":"Ghorai, G., Pal, M.: Faces and dual of m-polar fuzzy planar graphs. J. Intell. Fuzzy Syst. 31(3), 2043\u20132049 (2016)","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"3","key":"626_CR7","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1504\/IJCSM.2016.077854","volume":"7","author":"G Ghorai","year":"2016","unstructured":"Ghorai, G., Pal, M.: A study on m-polar fuzzy planar graphs. Int. J. Comput. Sci. Math.Comput. Sci. Math. 7(3), 283\u2013292 (2016)","journal-title":"Int. J. Comput. Sci. Math.Comput. Sci. Math."},{"key":"626_CR8","first-page":"215","volume":"38","author":"HJ Fleischner","year":"1974","unstructured":"Fleischner, H.J., Geller, D.P., Harary, F.: Outerplanar graphs and weak duals. J. Indian Math. Soc. 38, 215\u2013219 (1974)","journal-title":"J. Indian Math. Soc."},{"key":"626_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2","volume-title":"Graph Theory with Applications","author":"JA Bondy","year":"1976","unstructured":"Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications, vol. 290. Macmillan, London (1976)"},{"issue":"7","key":"626_CR10","first-page":"35","volume":"109","author":"K Shriram","year":"2016","unstructured":"Shriram, K., Sujatha, R., Narasimman, S.: Fuzzy combinatorial dual graphs. Int. J. Pure Appl. Math. 109(7), 35\u201341 (2016)","journal-title":"Int. J. Pure Appl. Math."},{"issue":"9","key":"626_CR11","doi-asserted-by":"publisher","first-page":"5059","DOI":"10.1007\/s00521-018-3948-5","volume":"32","author":"K Shriram","year":"2020","unstructured":"Shriram, K., Sujatha, R., Narasimman, S., Sundareswaran, R., Said, B.: Embedding of fuzzy graphs on topological surfaces. Neural Comput. Appl.Comput. Appl. 32(9), 5059\u20135069 (2020)","journal-title":"Neural Comput. Appl.Comput. Appl."},{"key":"626_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.dajour.2023.100339","volume":"9","author":"S Kalathian","year":"2023","unstructured":"Kalathian, S., Ramalingam, S., Deivanayagampillai, N.: A fuzzy planar subgraph formation model for partitioning very large-scale integration networks. Decis. Anal. J. 9, 100339 (2023)","journal-title":"Decis. Anal. J."},{"key":"626_CR13","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1007\/s40819-016-0132-4","volume":"3","author":"M Akram","year":"2017","unstructured":"Akram, M., Samanta, S., Pal, M.: Application of bipolar fuzzy sets in planar graphs. Int. J. Appl. Comput. Math. 3, 773\u2013785 (2017)","journal-title":"Int. J. Appl. Comput. Math."},{"key":"626_CR14","first-page":"675","volume":"26","author":"MM Sys\u0142o","year":"1978","unstructured":"Sys\u0142o, M.M.: Outerplanar graphs: characterizations, testing, coding, and counting. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys. 26, 675\u2013684 (1978)","journal-title":"Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys."},{"issue":"1","key":"626_CR15","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/0012-365X(79)90060-8","volume":"26","author":"MM Sys\u0142o","year":"1979","unstructured":"Sys\u0142o, M.M.: Characterizations of outerplanar graphs. Discret. Math.. Math. 26(1), 47\u201353 (1979)","journal-title":"Discret. Math.. Math."},{"issue":"1","key":"626_CR16","doi-asserted-by":"publisher","first-page":"37","DOI":"10.3233\/IDA-1999-3104","volume":"3","author":"MR Berthold","year":"1999","unstructured":"Berthold, M.R., Huber, K.P.: Constructing fuzzy graphs from examples. Intell. Data Anal. 3(1), 37\u201353 (1999)","journal-title":"Intell. Data Anal."},{"issue":"1","key":"626_CR17","first-page":"261","volume":"2","author":"MM Sys\u0142o","year":"1978","unstructured":"Sys\u0142o, M.M., Iri, M.: Efficient outerplanarity testing. Fund. Inform. 2(1), 261\u2013275 (1978)","journal-title":"Fund. Inform."},{"issue":"1","key":"626_CR18","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/0304-3975(82)90133-5","volume":"17","author":"MM Sys\u0142o","year":"1982","unstructured":"Sys\u0142o, M.M.: The subgraph isomorphism problem for outerplanar graphs. Theor. Comput. Sci.. Comput. Sci. 17(1), 91\u201397 (1982)","journal-title":"Theor. Comput. Sci.. Comput. Sci."},{"issue":"4","key":"626_CR19","first-page":"168","volume":"12","author":"N Abdul-Jabbar","year":"2009","unstructured":"Abdul-Jabbar, N., Naoom, J.H., Ouda, E.H.: Fuzzy dual graph. J. Al-Nahrain Univ. 12(4), 168\u2013171 (2009)","journal-title":"J. Al-Nahrain Univ."},{"key":"626_CR20","doi-asserted-by":"publisher","first-page":"693","DOI":"10.1007\/s12190-020-01411-x","volume":"65","author":"R Mahapatra","year":"2021","unstructured":"Mahapatra, R., Samanta, S., Pal, M.: Generalized neutrosophic planar graphs and its application. J. Appl. Math. Comput.Comput. 65, 693\u2013712 (2021)","journal-title":"J. Appl. Math. Comput.Comput."},{"key":"626_CR21","unstructured":"Samanta, S., Pal, A., Pal, M.: Concept of fuzzy planar graphs. In: Processing of Science and Information Conference, 7\u20139, 2013, pp. 557\u2013563 (2013)"},{"issue":"1","key":"626_CR22","doi-asserted-by":"publisher","first-page":"52","DOI":"10.14569\/IJARAI.2014.030108","volume":"3","author":"S Samanta","year":"2014","unstructured":"Samanta, S., Pal, M., Pal, A.: New concepts of fuzzy planar graph. Int. J. Adv. Res. Artif. Intell. 3(1), 52\u201359 (2014)","journal-title":"Int. J. Adv. Res. Artif. Intell."},{"issue":"6","key":"626_CR23","doi-asserted-by":"publisher","first-page":"1936","DOI":"10.1109\/TFUZZ.2014.2387875","volume":"23","author":"S Samanta","year":"2016","unstructured":"Samanta, S., Pal, M.: Fuzzy planar graphs. IEEE Trans. Fuzzy Syst. 23(6), 1936\u20131942 (2016)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"3","key":"626_CR24","doi-asserted-by":"publisher","first-page":"4273","DOI":"10.3233\/JIFS-190383","volume":"37","author":"S Rehmani","year":"2019","unstructured":"Rehmani, S., Sunitha, M.S.: Edge geodesic number of a fuzzy graph. J. Intell. Fuzzy Syst. 37(3), 4273\u20134286 (2019)","journal-title":"J. Intell. Fuzzy Syst."},{"key":"626_CR25","first-page":"475","volume":"4","author":"S Ramya","year":"2017","unstructured":"Ramya, S., Lavanya, S.: Edge contraction on bipolar fuzzy graphs. Int. J. Trend Res. Dev. 4, 475\u2013477 (2017)","journal-title":"Int. J. Trend Res. Dev."},{"issue":"1","key":"626_CR26","first-page":"133","volume":"13","author":"S Ramya","year":"2023","unstructured":"Ramya, S., Lavanya, S.: Contraction and domination in fuzzy graphs. TWMS J. Appl. Eng. Math. 13(1), 133\u2013142 (2023)","journal-title":"TWMS J. Appl. Eng. Math."},{"issue":"4","key":"626_CR27","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1007\/s13042-014-0284-7","volume":"7","author":"T Pramanik","year":"2016","unstructured":"Pramanik, T., Samanta, S., Pal, M.: Interval- valued fuzzy planar graphs. Int. J. Mach. Learn. Cybern.Cybern. 7(4), 653\u2013664 (2016)","journal-title":"Int. J. Mach. Learn. Cybern.Cybern."},{"key":"626_CR28","doi-asserted-by":"publisher","first-page":"1649","DOI":"10.1007\/s10462-020-09879-6","volume":"54","author":"T Mahapatra","year":"2021","unstructured":"Mahapatra, T., Sahoo, S., Ghorai, G., Pal, M.: Interval valued m-polar fuzzy planar graph and its application. Artif. Intell. Rev.. Intell. Rev. 54, 1649\u20131675 (2021)","journal-title":"Artif. Intell. Rev.. Intell. Rev."},{"key":"626_CR29","doi-asserted-by":"publisher","first-page":"138399","DOI":"10.1109\/ACCESS.2023.3339220","volume":"11","author":"U Mondal","year":"2023","unstructured":"Mondal, U., Mahapatra, T., Xin, Q., Pal, M.: Generalized m-Polar Fuzzy Planar Graph and Its Application. IEEE Access 11, 138399\u2013138413 (2023)","journal-title":"IEEE Access"},{"issue":"18\u201319","key":"626_CR30","doi-asserted-by":"publisher","first-page":"2044","DOI":"10.1016\/j.disc.2011.04.035","volume":"311","author":"H Lu","year":"2011","unstructured":"Lu, H., Wang, W., Bai, B.: Vertex deleted and regular factors from regular graph. Discret. Math.. Math. 311(18\u201319), 2044\u20132048 (2011)","journal-title":"Discret. Math.. Math."}],"container-title":["International Journal of Computational Intelligence Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-024-00626-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44196-024-00626-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44196-024-00626-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T17:17:06Z","timestamp":1725902226000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44196-024-00626-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,3]]},"references-count":30,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["626"],"URL":"https:\/\/doi.org\/10.1007\/s44196-024-00626-1","relation":{},"ISSN":["1875-6883"],"issn-type":[{"value":"1875-6883","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,3]]},"assertion":[{"value":"30 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This study did not involve human or animal subjects.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"All the authors agree with this manuscript\u2019s publication.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"231"}}