{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T19:46:12Z","timestamp":1774381572105,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T00:00:00Z","timestamp":1718323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A mathematical method of combining several elements has emerged in recent times, providing a more comprehensive approach. Adhering to the foregoing mathematical methodology, we fuse two extremely potent methods, namely graph theory and neutrosophic sets, and present the concept of neutrosophic graphs (\u2135G). Next, we outline many ideas, such as union, join, and composition of \u2135Gs, which facilitate the straightforward manipulation of \u2135Gs in decision-making scenarios. We provide a few scenarios to clarify these activities. The homomorphisms of \u2135Gs are also described. Lastly, understanding neutrosophic graphs and how Japan responds to earthquakes can help develop more resilient and adaptable disaster management plans, which can eventually save lives and lessen the effects of seismic disasters. With the support of using an absolute score function value, Hokkaido (H) and Saitama (SA) were the optimized locations. Because of its location in the Pacific Ring of Fire, Japan is vulnerable to regular earthquakes. As such, it is critical to customize reaction plans to the unique difficulties and features of Japan\u2019s seismic activity. Examining neutrosophic graphs within the framework of earthquake response centers might offer valuable perspectives on tailoring and enhancing response tactics, particularly for Japan\u2019s requirements.<\/jats:p>","DOI":"10.3390\/sym16060743","type":"journal-article","created":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T08:52:10Z","timestamp":1718355130000},"page":"743","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Study on Neutrosophic Graph with Application on Earthquake Response Center in Japan"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6872-1838","authenticated-orcid":false,"given":"Wadei Faris","family":"AL-Omeri","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4709-1857","authenticated-orcid":false,"given":"M.","family":"Kaviyarasu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Vel Tech Rangarajan Dr Sagunthala R & D Institute of Science and Technology, Chennai 600062, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,14]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","unstructured":"Atanassov Krassimir, T. (2019). Intuitionistic fuzzy sets. Intuitionistic Fuzzy Sets, Springer.","DOI":"10.1007\/978-3-030-32090-4_2"},{"key":"ref_3","unstructured":"Smarandache, F. (1999). A unifying field in logics: Neutrosophic logic. Philosophy, American Research Press."},{"key":"ref_4","unstructured":"Smarandache, F. (2007). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, InfoLearnQuest. [6th ed.]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3681","DOI":"10.3233\/IFS-162114","article-title":"Regularity of vague graphs","volume":"30","author":"Borzooei","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_6","first-page":"27","article-title":"Certain types of edge m-polar fuzzy graphs","volume":"14","author":"Waseem","year":"2017","journal-title":"Iran. J. Fuzzy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1007\/s40819-015-0112-0","article-title":"Certain types of product bipolar fuzzy graphs","volume":"3","author":"Ghorai","year":"2017","journal-title":"Int. J. Appl. Comput. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2137","DOI":"10.3233\/JIFS-161944","article-title":"Operations on single valued \u2135Gs with application","volume":"32","author":"Naz","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_9","first-page":"87","article-title":"Different types of products on intuitionistic fuzzy graphs","volume":"17","author":"Sahoo","year":"2015","journal-title":"Pac. Sci. Rev. A Nat. Sci. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.3233\/IFS-151827","article-title":"On single valued neutrosophic relations","volume":"30","author":"Yang","year":"2006","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_11","first-page":"311","article-title":"Single-valued neutrosophic minimum spanning tree and its clustering method","volume":"23","author":"Ye","year":"2014","journal-title":"J. Intell. Syst."},{"key":"ref_12","first-page":"24","article-title":"On a generalization of intuitionistic fuzzy graphs","volume":"12","author":"Shannon","year":"2006","journal-title":"NIFS"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Parvathi, R., and Karunambigai, M.G. (2006). Intuitionistic fuzzy graphs. Computational Intelligence, Theory and Applications, Springer.","DOI":"10.1007\/3-540-34783-6_15"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Parvathi, R., Karunambigai, M.G., and Atanassov, K.T. (2009, January 20\u201324). Operations on intuitionistic fuzzy graphs. Proceedings of the 2009 IEEE International Conference on Fuzzy Systems, Jeju, Republic of Korea.","DOI":"10.1109\/FUZZY.2009.5277067"},{"key":"ref_15","first-page":"39","article-title":"Domination in intuitionistic fuzzy graphs","volume":"16","author":"Parvathi","year":"2010","journal-title":"Notes Intuit Fuzzy Sets"},{"key":"ref_16","first-page":"30","article-title":"Properties of interval valued intuitionistic (s, t)\u2013fuzzy graphs","volume":"18","author":"Rashmanlou","year":"2016","journal-title":"Pac. Sci. Rev. A Nat. Sci. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1080\/18756891.2015.1063243","article-title":"Bipolar fuzzy graphs with categorical properties","volume":"8","author":"Rashmanlou","year":"2015","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.fiae.2015.09.005","article-title":"Intuitionistic fuzzy graphs with categorical properties","volume":"7","author":"Rashmanlou","year":"2015","journal-title":"Fuzzy Inf. Eng."},{"key":"ref_19","first-page":"290","article-title":"Extension of hypergraph to n-superhypergraph and to plithogenic n-superhypergraph, and extension of hyperalgebra to n-ary hyperalgebra","volume":"33","author":"Smarandache","year":"2020","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.22342\/jims.24.1.455.1-25","article-title":"Certain bipolar neutrosophic competition graphs","volume":"24","author":"Akram","year":"2017","journal-title":"J. Indones. Math. Soc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/j.fiae.2017.01.001","article-title":"Operations on intuitionistic fuzzy graph structures","volume":"8","author":"Akram","year":"2016","journal-title":"Fuzzy Inf. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s40747-018-0089-5","article-title":"Certain graphs under pythagorean fuzzy environment","volume":"5","author":"Akram","year":"2019","journal-title":"Complex Intell. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Akram, M., Habib, A., Ilyas, F., and Dar, J.M. (2018). Specific types of pythagorean fuzzy graphs and application to decision-making. Math. Comput. Appl., 23.","DOI":"10.3390\/mca23030042"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Akram, M., and Naz, S. (2018). Energy of pythagorean fuzzy graphs with applications. Mathematics, 6.","DOI":"10.3390\/math6080136"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"921","DOI":"10.3233\/JIFS-162207","article-title":"Neutrosophic competition graphs with applications","volume":"33","author":"Akram","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Smarandache, F., and Abdel-Basset, M. (2021). The Determinant and Adjoint of an Interval-Valued Neutrosophic Matrix. Neutrosophic Operational Research, Springer.","DOI":"10.1007\/978-3-030-57197-9"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8535703","DOI":"10.1155\/2018\/8535703","article-title":"Characterizations of Certain Types of Type 2 Soft Graphs","volume":"2018","author":"Hayat","year":"2018","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4594","DOI":"10.1007\/s10489-018-1226-y","article-title":"Some new operations on single-valued neutrosophic matrices and their applications in multi-criteria group decision making","volume":"48","author":"Karaaslan","year":"2018","journal-title":"Appl. Intell."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"060024","DOI":"10.1063\/5.0157832","article-title":"Topological indices of certain neutrosophic graphs","volume":"2845","author":"Majeed","year":"2023","journal-title":"Aip Conf. Proc."},{"key":"ref_30","first-page":"239","article-title":"On r-Edge Regular Neutrosophic Graphs","volume":"53","author":"Kaviyarasu","year":"2023","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_31","first-page":"257","article-title":"Identifying Internet Streaming Services using Max Product of Complement in Neutrosophic Graphs","volume":"3","author":"Kaviyarasu","year":"2024","journal-title":"Int. J. Neutrosophic Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Yaqoob, N., Gulistan, M., Kadry, S., and Wahab, H.A. (2019). Complex Intuitionistic Fuzzy Graphs with Application in Cellular Network Provider Companies. Mathematics, 7.","DOI":"10.3390\/math7010035"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1699","DOI":"10.2991\/ijcis.d.201015.002","article-title":"Link Prediction in Social Networks by Neutrosophic Graph","volume":"13","author":"Mahapatra","year":"2020","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_34","first-page":"5286","article-title":"An approximation of balanced score in neutrosophic graphs with weak edge weights","volume":"11","author":"Srisarkun","year":"2021","journal-title":"Int. J. Electr. Comput. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1149724","DOI":"10.1155\/2022\/1149724","article-title":"Edge Colouring of Neutrosophic Graphs and Its Application in Detection of Phishing Website","volume":"2022","author":"Mahapatra","year":"2022","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s40314-022-01823-4","article-title":"New concepts of pentapartitioned neutrosophic graphs and applications for determining safest paths and towns in response to COVID-19","volume":"41","author":"Quek","year":"2022","journal-title":"Comp. Appl. Math."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Alqahtani, M., Kaviyarasu, M., Al-Masarwah, A., and Rajeshwari, M. (2024). Application of Complex Neutrosophic Graphs in Hospital Infrastructure Design. Mathematics, 12.","DOI":"10.3390\/math12050719"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/j.ins.2014.05.012","article-title":"An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets","volume":"280","author":"Wang","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_39","first-page":"338","article-title":"Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment","volume":"280","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_40","first-page":"248","article-title":"Theory and Applications of Fermatean Neutrosophic Graphs","volume":"50","author":"Broumi","year":"2002","journal-title":"Neutrosophic Sets Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/6\/743\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:58:45Z","timestamp":1760108325000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/6\/743"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,14]]},"references-count":40,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["sym16060743"],"URL":"https:\/\/doi.org\/10.3390\/sym16060743","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,14]]}}}