{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T05:51:32Z","timestamp":1780984292823,"version":"3.54.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T00:00:00Z","timestamp":1715817600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T00:00:00Z","timestamp":1715817600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2024,8]]},"DOI":"10.1007\/s12190-024-02117-0","type":"journal-article","created":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T12:01:56Z","timestamp":1715860916000},"page":"3825-3850","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Fuzzy graphs in telecommunications: exploring average fuzzy cyclic connectivity for enhanced connectivity analysis"],"prefix":"10.1007","volume":"70","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6260-2547","authenticated-orcid":false,"given":"P.","family":"Sujithra","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sunil","family":"Mathew","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. N.","family":"Mordeson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,5,16]]},"reference":[{"key":"2117_CR1","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338\u2013353 (1965)","journal-title":"Inf. Control"},{"key":"2117_CR2","unstructured":"Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L. A., Fu, K.S., Shimura M. (Eds.), Fuzzy Sets and Their Applications to Cognitive and Decision Processes, Academic Press, pp 77-95 (1975)"},{"key":"2117_CR3","unstructured":"Bang, S. Y., Yeh, R. T.: Fuzzy relations, fuzzy graphs and their applications to clustering analysis. In: Zadeh, L. A., Fu, K. S., Shimura, M. (Eds.), Fuzzy Sets and their Applications, Academic Press, pp 125-149 (1975)"},{"key":"2117_CR4","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/0167-8655(91)90307-8","volume":"12","author":"P Bhattacharya","year":"1991","unstructured":"Bhattacharya, P., Suraweera, F.: An algorithm to compute the supremum of max-min powers and a property of fuzzy graphs. Pattern Recognit. Lett. 12, 413\u2013420 (1991)","journal-title":"Pattern Recognit. Lett."},{"key":"2117_CR5","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1016\/0167-8655(87)90012-2","volume":"6","author":"P Bhattacharya","year":"1987","unstructured":"Bhattacharya, P.: Some remarks on fuzzy graphs. Pattern Recognit. Lett. 6, 297\u2013302 (1987)","journal-title":"Pattern Recognit. Lett."},{"key":"2117_CR6","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/S0020-0255(02)00411-5","volume":"152","author":"KR Bhutani","year":"2003","unstructured":"Bhutani, K.R., Rosenfeld, A.: Strong arcs in fuzzy graphs. Inf. Sci. 152, 319\u2013322 (2003)","journal-title":"Inf. Sci."},{"key":"2117_CR7","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/S0020-0255(03)00078-1","volume":"152","author":"KR Bhutani","year":"2003","unstructured":"Bhutani, K.R., Rosenfeld, A.: Fuzzy end nodes in fuzzy graphs. Inf. Sci. 152, 323\u2013326 (2003)","journal-title":"Inf. Sci."},{"key":"2117_CR8","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/0020-0255(95)00238-3","volume":"90","author":"JN Mordeson","year":"1996","unstructured":"Mordeson, J.N., Nair, P.S.: Cycles and cocycles of fuzzy graphs. Inf. Sci. 90, 39\u201349 (1996)","journal-title":"Inf. Sci."},{"key":"2117_CR9","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/S0020-0255(98)10066-X","volume":"113","author":"MS Sunitha","year":"1999","unstructured":"Sunitha, M.S., Vijayakumar, A.: A characterization of fuzzy trees. Inf. Sci. 113, 293\u2013300 (1999)","journal-title":"Inf. Sci."},{"key":"2117_CR10","doi-asserted-by":"publisher","first-page":"1760","DOI":"10.1016\/j.ins.2009.01.003","volume":"179","author":"S Mathew","year":"2009","unstructured":"Mathew, S., Sunitha, M.S.: Types of arcs in a fuzzy graph. Inf. Sci. 179, 1760\u20131768 (2009)","journal-title":"Inf. Sci."},{"key":"2117_CR11","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1016\/j.ins.2009.10.006","volume":"180","author":"S Mathew","year":"2010","unstructured":"Mathew, S., Sunitha, M.S.: Node connectivity and arc connectivity in fuzzy graphs. Inf. Sci. 180, 519\u2013531 (2010)","journal-title":"Inf. Sci."},{"key":"2117_CR12","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1016\/j.ins.2012.07.026","volume":"222","author":"S Mathew","year":"2013","unstructured":"Mathew, S., Sunitha, M.S.: Menger\u2019s theorem for fuzzy graphs. Inf. Sci. 222, 717\u2013726 (2013)","journal-title":"Inf. Sci."},{"key":"2117_CR13","doi-asserted-by":"publisher","first-page":"549","DOI":"10.3233\/IFS-2012-0573","volume":"24","author":"S Mathew","year":"2013","unstructured":"Mathew, S., Sunitha, M.S.: Cycle connectivity in fuzzy graphs. J. Intell. Fuzzy Syst. 24, 549\u2013554 (2013)","journal-title":"J. Intell. Fuzzy Syst."},{"key":"2117_CR14","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/j.fiae.2015.05.008","volume":"7","author":"N Jicy","year":"2015","unstructured":"Jicy, N., Mathew, S.: Connectivity analysis of cyclically balanced fuzzy graphs. Fuzzy Inf. Eng. 7, 245\u2013255 (2015)","journal-title":"Fuzzy Inf. Eng."},{"key":"2117_CR15","doi-asserted-by":"crossref","unstructured":"Prabhath, A., Mathew, S., Mordeson, J. N.: Generalized cycle connectivity in fuzzy graphs. Fuzzy Sets Syst. 482, (2024)","DOI":"10.1016\/j.fss.2024.108909"},{"key":"2117_CR16","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/j.fiae.2015.09.005","volume":"7","author":"H Rashmanlou","year":"2015","unstructured":"Rashmanlou, H., Samanta, S., Pal, M., Borzooei, R.A.: Intuitionistic fuzzy graphs with categorical properties. Fuzzy Inf. Eng. 7, 317\u2013334 (2015)","journal-title":"Fuzzy Inf. Eng."},{"key":"2117_CR17","first-page":"4007","volume":"33","author":"S Sahoo","year":"2017","unstructured":"Sahoo, S., Pal, M., Rashmanlou, H., Borzooei, R.A.: Covering and paired domination in intuitionistic fuzzy graphs. J. Int. Fuzzy Syst. 33, 4007\u20134015 (2017)","journal-title":"J. Int. Fuzzy Syst."},{"key":"2117_CR18","doi-asserted-by":"crossref","unstructured":"Samanta, S., Sarkar, B., Shin, D., Pal, M.: Completeness and regularity of generalized fuzzy graphs, Springer plus. 5, (2016)","DOI":"10.1186\/s40064-016-3558-6"},{"issue":"6","key":"2117_CR19","doi-asserted-by":"publisher","first-page":"1340","DOI":"10.1109\/TFUZZ.2020.2973941","volume":"29","author":"M Binu","year":"2021","unstructured":"Binu, M., Mathew, S., Mordeson, J.N.: Cyclic connectivity index of fuzzy graphs. IEEE Trans. Fuzzy Syst. 29(6), 1340\u20131349 (2021)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"2117_CR20","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/j.fss.2019.01.022","volume":"384","author":"M Binu","year":"2020","unstructured":"Binu, M., Mathew, S., Mordeson, J.N.: Wiener index of a fuzzy graph and application to illegal immigration networks. Fuzzy Sets Syst. 384, 132\u2013147 (2020)","journal-title":"Fuzzy Sets Syst."},{"key":"2117_CR21","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1016\/j.ins.2021.05.068","volume":"573","author":"M Binu","year":"2021","unstructured":"Binu, M., Mathew, S., Mordeson, J.N.: Connectivity status of fuzzy graphs. Inf. Sci. 573, 382\u2013395 (2021)","journal-title":"Inf. Sci."},{"key":"2117_CR22","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.fss.2018.06.007","volume":"360","author":"M Binu","year":"2019","unstructured":"Binu, M., Mathew, S., Mordeson, J.N.: Connectivity index of a fuzzy graph and its application to human trafficking. Fuzzy Sets Syst. 360, 117\u2013136 (2019)","journal-title":"Fuzzy Sets Syst."},{"key":"2117_CR23","first-page":"1","volume":"37","author":"R Mahapatra","year":"2019","unstructured":"Mahapatra, R., Samanta, S., Pal, M., Xin, Q.: RSM index: A new way of link prediction in social networks. J. Int. Fuzzy Syst. 37, 1\u201315 (2019)","journal-title":"J. Int. Fuzzy Syst."},{"key":"2117_CR24","doi-asserted-by":"publisher","first-page":"2232","DOI":"10.1016\/j.disc.2013.05.024","volume":"313","author":"J Kim","year":"2013","unstructured":"Kim, J., Suil, O.: Average connectivity and average edge-connectivity in graphs. Discret. Math. 313, 2232\u20132238 (2013)","journal-title":"Discret. Math."},{"key":"2117_CR25","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/S0012-365X(01)00180-7","volume":"252","author":"L Beineke","year":"2002","unstructured":"Beineke, L., Oellermann, O., Pippert, R.: The average connectivity of a graph. Discret. Math. 252, 31\u201345 (2002)","journal-title":"Discret. Math."},{"key":"2117_CR26","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1142\/S1793005718500278","volume":"14","author":"S Ali","year":"2018","unstructured":"Ali, S., Mathew, S., Mordeson, J.N., Rashmanlou, H.: Vertex connectivity of fuzzy graphs with applications to human trafficking. New Math. Nat. Comput. 14, 457\u2013485 (2018)","journal-title":"New Math. Nat. Comput."},{"key":"2117_CR27","doi-asserted-by":"crossref","unstructured":"Mordeson, J. N., Mathew, S., Malik, D. S.: Fuzzy Graph Theory with Applications to Human Trafficking. Springer (2018)","DOI":"10.1007\/978-3-319-76454-2"},{"key":"2117_CR28","doi-asserted-by":"crossref","unstructured":"Pal, M., Samanta, S., Ghorai, G.: Modern Trends in Fuzzy Graph Theory. Springer (2020)","DOI":"10.1007\/978-981-15-8803-7"},{"key":"2117_CR29","first-page":"189","volume":"10","author":"JN Mordeson","year":"2002","unstructured":"Mordeson, J.N., Yao, Y.Y.: Fuzzy cycles and fuzzy trees. J. Fuzzy Math. 10, 189\u2013202 (2002)","journal-title":"J. Fuzzy Math."},{"key":"2117_CR30","doi-asserted-by":"publisher","first-page":"1096","DOI":"10.1109\/TFUZZ.2013.2243154","volume":"6","author":"S Mathew","year":"2013","unstructured":"Mathew, S., Sunitha, M.S.: Strongest strong cycles and $$\\theta $$-fuzzy graphs. IEEE Trans. Fuzzy Syst. 6, 1096\u20131104 (2013)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"2117_CR31","doi-asserted-by":"crossref","unstructured":"Mordeson, J. N., Nair, P. S.: Arc disjoint fuzzy graphs, IEEE, pp. 65-69 (1999)","DOI":"10.1109\/NAFIPS.1999.781654"},{"key":"2117_CR32","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1002\/net.1975.5.3.237","volume":"5","author":"RC Read","year":"1975","unstructured":"Read, R.C., Tarjan, R.E.: Bounds on backtrack algorithms for listing cycles, paths and spanning trees. Networks 5, 237\u2013252 (1975)","journal-title":"Networks"},{"key":"2117_CR33","unstructured":"Anti-Phishing Working Group. https:\/\/apwg.org\/reportphishing\/"},{"key":"2117_CR34","unstructured":"Business Email Compromise (BEC). https:\/\/www.fbi.gov\/how-we-can-help-you\/safety-resources\/scams-and-safety\/common-scams-and-crimes\/business-email-compromise"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-024-02117-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-024-02117-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-024-02117-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T05:42:38Z","timestamp":1731994958000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-024-02117-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,16]]},"references-count":34,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["2117"],"URL":"https:\/\/doi.org\/10.1007\/s12190-024-02117-0","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,16]]},"assertion":[{"value":"2 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 April 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2024","order":4,"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 that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}