{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T04:34:14Z","timestamp":1776918854793,"version":"3.51.2"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"14","license":[{"start":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T00:00:00Z","timestamp":1571875200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,10,24]],"date-time":"2019-10-24T00:00:00Z","timestamp":1571875200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2020,7]]},"DOI":"10.1007\/s00521-019-04563-5","type":"journal-article","created":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T18:59:41Z","timestamp":1572029981000},"page":"10263-10273","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Domination integrity and efficient fuzzy graphs"],"prefix":"10.1007","volume":"32","author":[{"given":"Saravanan","family":"Mariappan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sujatha","family":"Ramalingam","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sundareswaran","family":"Raman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Goksen","family":"Bacak-Turan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,10,24]]},"reference":[{"key":"4563_CR1","volume-title":"Theory of graphs","author":"O Ore","year":"1962","unstructured":"Ore O (1962) Theory of graphs. American Mathematical Society, Providence"},{"key":"4563_CR2","first-page":"12","volume":"1","author":"CA Barefoot","year":"1987","unstructured":"Barefoot CA, Entringer R, Swart H (1987) Vulnerability in graphs\u2014a comparative survey. J Combin Math Combin Comput 1:12\u201322","journal-title":"J Combin Math Combin Comput"},{"key":"4563_CR3","first-page":"103","volume":"58","author":"CA Barefoot","year":"1987","unstructured":"Barefoot CA, Entringer R, Swart H (1987) Integrity of trees and powers of cycles. Congr Numer 58:103\u2013114","journal-title":"Congr Numer"},{"key":"4563_CR4","unstructured":"Goddard W (1989) On the vulnerability of graphs, Ph.D. Thesis, University of Natal, Durban, SA"},{"key":"4563_CR5","first-page":"139","volume":"7","author":"W Goddard","year":"1990","unstructured":"Goddard W, Swart HC (1990) Integrity in graphs: bounds and basics. J Combin Math Combin 7:139\u2013151","journal-title":"J Combin Math Combin"},{"key":"4563_CR6","first-page":"3","volume":"4","author":"W Goddard","year":"1988","unstructured":"Goddard W, Swart HC (1988) On the integrity of combinations of graphs. J Combin Math Combin Comput 4:3\u201318","journal-title":"J Combin Math Combin Comput"},{"issue":"38","key":"4563_CR7","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0166-218X(92)90122-Q","volume":"37","author":"KS Bagga","year":"1992","unstructured":"Bagga KS, Beineke LW, Goddard WD, Lipman MJ, Pipert RE (1992) A survey of integrity. Discret Appl Math 37(38):13\u201328","journal-title":"Discret Appl Math"},{"issue":"5","key":"4563_CR8","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1023\/B:MATN.0000049665.92885.26","volume":"75","author":"P Dundar","year":"2004","unstructured":"Dundar P, Aytac A (2004) Integrity of total graphs via certain parameters. Math Notes 75(5):665\u2013672","journal-title":"Math Notes"},{"key":"4563_CR9","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1007\/978-3-540-70666-3_14","volume":"4381","author":"A Mamut","year":"2007","unstructured":"Mamut A, Vumar E (2007) A note on the integrity of middle graphs. Lect Notes Comput Sci 4381:130\u2013134","journal-title":"Lect Notes Comput Sci"},{"key":"4563_CR10","first-page":"57","volume":"5","author":"SS Mahde","year":"2015","unstructured":"Mahde SS, Mathad V, Sahal AM (2015) Hub-integrity of graphs. Bull Int Math Virtual Inst 5:57\u201364","journal-title":"Bull Int Math Virtual Inst"},{"key":"4563_CR11","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0012-365X(94)90084-1","volume":"124","author":"KS Bagga","year":"1994","unstructured":"Bagga KS, Beineke LW, Lipman MJ, Pippert RE (1994) Edge-integrity: a survey. Discret Math 124:3\u201312","journal-title":"Discret Math"},{"issue":"7","key":"4563_CR12","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1080\/00207160412331336062","volume":"82","author":"Y Li","year":"2005","unstructured":"Li Y, Zhang S, Li X (2005) Rupture degree of graphs. Int J Comput Math 82(7):793\u2013803","journal-title":"Int J Comput Math"},{"issue":"2","key":"4563_CR13","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0095-8956(78)90013-8","volume":"24","author":"HA Jung","year":"1978","unstructured":"Jung HA (1978) On a class of posets and the corresponding comparability graphs. J Combin Theory Ser B 24(2):125\u2013133","journal-title":"J Combin Theory Ser B"},{"key":"4563_CR14","first-page":"1111","volume-title":"Graph theory, combinatorics, and algorithms","author":"M Cozzens","year":"1992","unstructured":"Cozzens M, Moazzami D, Stueckle S (1992) The tenacity of a graph. Graph theory, combinatorics, and algorithms, vol 1, 2. Wiley, New York, pp 1111\u20131122"},{"key":"4563_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00373-006-0649-0","volume":"22","author":"D Bauer","year":"2006","unstructured":"Bauer D, Broersma H, Schmeichel E (2006) Toughness in graphs: a survey. Graphs Combin 22:1\u201335. https:\/\/doi.org\/10.1007\/s00373-006-0649-0","journal-title":"Graphs Combin"},{"key":"4563_CR16","first-page":"46","volume":"3\u20138","author":"R Sundareswaran","year":"2009","unstructured":"Sundareswaran R, Swaminathan V (2009) Domination integrity in graphs. Proc Int Conf Math Exp Phys Prague 3\u20138:46\u201357","journal-title":"Proc Int Conf Math Exp Phys Prague"},{"key":"4563_CR17","first-page":"88","volume-title":"Algebra, graph theory and their applications","author":"R Sundareswaran","year":"2010","unstructured":"Sundareswaran R, Swaminathan V (2010) Domination integrity of middle graphs. In: Chelvam T, Somasundaram S, Kala R (eds) Algebra, graph theory and their applications. Narosa Publishing House, New Delhi, pp 88\u201392"},{"key":"4563_CR18","first-page":"153","volume":"2","author":"R Sundareswaran","year":"2010","unstructured":"Sundareswaran R, Swaminathan V (2010) Domination integrity in trees. Bull Int Math Virtual Inst 2:153\u2013161","journal-title":"Bull Int Math Virtual Inst"},{"issue":"3","key":"4563_CR19","first-page":"257","volume":"3","author":"R Sundareswaran","year":"2011","unstructured":"Sundareswaran R, Swaminathan V (2011) Domination integrity of powers of cycles. Int J Math Res 3(3):257\u2013265","journal-title":"Int J Math Res"},{"issue":"1","key":"4563_CR20","first-page":"54","volume":"6","author":"R Sundareswaran","year":"2016","unstructured":"Sundareswaran R, Swaminathan V (2016) Integrity and domination integrity of gear graphs. J Appl Eng Math 6(1):54\u201364","journal-title":"J Appl Eng Math"},{"key":"4563_CR21","first-page":"377","volume":"23","author":"E Sampathkumar","year":"1989","unstructured":"Sampathkumar E (1989) The global domination number of a graph. J Math Phys Sci 23:377\u2013385","journal-title":"J Math Phys Sci"},{"key":"4563_CR22","doi-asserted-by":"crossref","first-page":"263","DOI":"10.18576\/msl\/060307","volume":"6","author":"SS Mahde","year":"2017","unstructured":"Mahde SS, Mathad V (2017) Global domination integrity of graphs. Math Sci Lett 6:263\u2013269","journal-title":"Math Sci Lett"},{"issue":"3","key":"4563_CR23","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338\u2013353","journal-title":"Inf Control"},{"key":"4563_CR24","first-page":"77","volume-title":"Fuzzy sets and their applications","author":"A Rosenfeld","year":"1975","unstructured":"Rosenfeld A (1975) Fuzzy graphs. In: Zadeh LA, Fu KS, Shimura M (eds) Fuzzy sets and their applications. Academic press, New york, pp 77\u201395"},{"key":"4563_CR25","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/S0020-0255(02)00411-5","volume":"152","author":"KR Bhutani","year":"2003","unstructured":"Bhutani KR, Rosenfeld A (2003) Strong arcs in fuzzy graphs. Inf Sci 152:319\u2013322","journal-title":"Inf Sci"},{"key":"4563_CR26","doi-asserted-by":"crossref","first-page":"1760","DOI":"10.1016\/j.ins.2009.01.003","volume":"179","author":"S Mathew","year":"2009","unstructured":"Mathew S, Sunitha MS (2009) Types of arcs in a fuzzy graphs. Inf Sci 179:1760\u20131768","journal-title":"Inf Sci"},{"key":"4563_CR27","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/S0167-8655(98)00064-6","volume":"19","author":"A Somasundaram","year":"1998","unstructured":"Somasundaram A, Somasundaram S (1998) Domination in fuzzy graphs-I. Pattern Recognit Lett 19:787\u2013791","journal-title":"Pattern Recognit Lett"},{"issue":"2","key":"4563_CR28","first-page":"281","volume":"13","author":"A Somasundaram","year":"2005","unstructured":"Somasundaram A (2005) Domination in fuzzy graphs\u2014II. J Fuzzy Math 13(2):281\u2013288","journal-title":"J Fuzzy Math"},{"issue":"1","key":"4563_CR29","first-page":"17","volume":"I","author":"A Nagoorgani","year":"2006","unstructured":"Nagoorgani A, Chandrasekaran VT (2006) Domination in fuzzy graph. Adv Fuzzy Sets Syst I(1):17\u201326","journal-title":"Adv Fuzzy Sets Syst"},{"issue":"26","key":"4563_CR30","first-page":"1303","volume":"6","author":"A Nagoorgani","year":"2011","unstructured":"Nagoorgani A, Vijayalakshmi P (2011) Insensitive arc in domination of fuzzy graph. Int J Contemp Math Sci 6(26):1303\u20131309","journal-title":"Int J Contemp Math Sci"},{"issue":"6","key":"4563_CR31","doi-asserted-by":"publisher","first-page":"3205","DOI":"10.3233\/IFS-141277","volume":"27","author":"OT Manjusha","year":"2014","unstructured":"Manjusha OT, Sunitha MS (2014) Notes on domination in fuzzy graphs. J Intell Fuzzy Syst 27(6):3205\u20133212. https:\/\/doi.org\/10.3233\/IFS-141277","journal-title":"J Intell Fuzzy Syst"},{"key":"4563_CR32","volume-title":"Distance in fuzzy graphs","author":"S Kalathodi","year":"2012","unstructured":"Kalathodi S, Sunitha MS (2012) Distance in fuzzy graphs. LAP LAMBERT Academic Publishing, New York"},{"key":"4563_CR33","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.fiae.2015.09.007","volume":"7","author":"OT Manjusha","year":"2015","unstructured":"Manjusha OT, Sunitha MS (2015) Strong domination in fuzzy graphs. Fuzzy Int Eng 7:369\u2013377","journal-title":"Fuzzy Int Eng"},{"key":"4563_CR34","first-page":"89","volume":"6","author":"M Saravanan","year":"2016","unstructured":"Saravanan M, Sujatha R, Sundareswaran R (2016) Integrity of fuzzy graphs. Bull Int Math Virtual Inst 6:89\u201396","journal-title":"Bull Int Math Virtual Inst"},{"issue":"82","key":"4563_CR35","first-page":"160","volume":"10","author":"M Saravanan","year":"2015","unstructured":"Saravanan M, Sujatha R, Sundareswaran R (2015) A study of regular fuzzy graphs and integrity of fuzzy graphs. Int J Appl Eng Res 10(82):160\u2013164","journal-title":"Int J Appl Eng Res"},{"issue":"4","key":"4563_CR36","doi-asserted-by":"crossref","first-page":"2429","DOI":"10.3233\/JIFS-171685","volume":"34","author":"M Saravanan","year":"2018","unstructured":"Saravanan M, Sujatha R, Sundareswaran R (2018) Concept of integrity and its result in fuzzy graphs. J Intell Fuzzy Syst 34(4):2429\u20132439","journal-title":"J Intell Fuzzy Syst"},{"issue":"4","key":"4563_CR37","doi-asserted-by":"crossref","first-page":"2066","DOI":"10.3906\/elk-1711-242","volume":"26","author":"S Mariappan","year":"2018","unstructured":"Mariappan S, Ramalingam S, Raman S, Muthuselvan B (2018) Application of domination integrity of graphs in PMU placement in electric power networks. Turk J Electric Eng Comput Sci 26(4):2066\u20132076","journal-title":"Turk J Electric Eng Comput Sci"},{"issue":"6","key":"4563_CR38","doi-asserted-by":"publisher","first-page":"1936","DOI":"10.1109\/TFUZZ.2014.2387875","volume":"23","author":"S Samanta","year":"2015","unstructured":"Samanta S, Pal M (2015) Fuzzy planar graphs. IEEE Trans Fuzzy Syst 23(6):1936\u20131942. https:\/\/doi.org\/10.1109\/TFUZZ.2014.2387875","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"4563_CR39","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/s12543-013-0140-6S","volume":"5","author":"S Samanta","year":"2013","unstructured":"Samanta S, Pal M (2013) Fuzzy k-competition graphs and p-competition fuzzy graphs. Fuzzy Inf Eng 5(5):191\u2013204. https:\/\/doi.org\/10.1007\/s12543-013-0140-6S","journal-title":"Fuzzy Inf Eng"},{"issue":"1","key":"4563_CR40","doi-asserted-by":"crossref","first-page":"17","DOI":"10.5121\/ijfls.2012.2103","volume":"2","author":"S Samanta","year":"2012","unstructured":"Samanta S, Pal M (2012) Bipolar fuzzy hypergraphs. Int J Fuzzy Logic Syst 2(1):17\u201328","journal-title":"Int J Fuzzy Logic Syst"},{"key":"4563_CR41","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/s12190-014-0785-2","volume":"47","author":"S Samanta","year":"2015","unstructured":"Samanta S, Akram M, Pal M (2015) m-step fuzzy competition graphs. J Appl Math Comput 47:461\u2013472. https:\/\/doi.org\/10.1007\/s12190-014-0785-2","journal-title":"J Appl Math Comput"},{"key":"4563_CR42","first-page":"28","volume":"3","author":"H Rashmanlou","year":"2013","unstructured":"Rashmanlou H, Pal M (2013) Isometry on interval-valued fuzzy graphs. Int J Fuzzy Math Arch 3:28\u201335","journal-title":"Int J Fuzzy Math Arch"},{"key":"4563_CR43","first-page":"107","volume":"3","author":"H Rashmanlou","year":"2013","unstructured":"Rashmanlou H, Pal M (2013) Antipodal interval-valued fuzzy graphs. Int J Appl Fuzzy Sets Artif Intell 3:107\u2013130","journal-title":"Int J Appl Fuzzy Sets Artif Intell"},{"issue":"1","key":"4563_CR44","first-page":"56","volume":"3","author":"M Pal","year":"2013","unstructured":"Pal M, Rashmanlou H (2013) Irregular interval\u2014valued fuzzy graphs. Ann Pure Appl Math 3(1):56\u201366","journal-title":"Ann Pure Appl Math"},{"issue":"4","key":"4563_CR45","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/j.ins.2009.10.006","volume":"180","author":"S Mathew","year":"2010","unstructured":"Mathew S, Sunitha MS (2010) Node connectivity and arc connectivity of a fuzzy graph. Inf Sci 180(4):519\u2013531","journal-title":"Inf Sci"},{"key":"4563_CR46","doi-asserted-by":"crossref","first-page":"261","DOI":"10.3390\/math7030261","volume":"7","author":"D Sensarma","year":"2019","unstructured":"Sensarma D, Sen Sarma S (2019) Role of graphic integer sequence in the determination of graph integrity. Mathematics 7:261","journal-title":"Mathematics"},{"key":"4563_CR47","first-page":"1","volume-title":"Neural computing and applications","author":"S Kalathian","year":"2019","unstructured":"Kalathian S, Ramalingam S, Srinivasan N, Raman S, Broumi S (2019) Embedding of fuzzy graphs on topological surfaces. Neural computing and applications. Springer, New York, pp 1\u201311"},{"key":"4563_CR48","first-page":"1","volume-title":"Evolving systems","author":"Z Halim","year":"2018","unstructured":"Halim Z, Khattak JH (2018) Density-based clustering of big probabilistic graphs. Evolving systems. Springer, New York, pp 1\u201318"},{"key":"4563_CR49","doi-asserted-by":"crossref","unstructured":"Rashid A, Kamran M, Halim Z (2019) A top down approach to enumerate $$\\alpha$$-maximal cliques in uncertain graphs. J Intell Fuzzy Syst 1\u201313 (Preprint)","DOI":"10.3233\/JIFS-18263"},{"key":"4563_CR50","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.ijar.2017.07.013","volume":"90","author":"Z Halim","year":"2017","unstructured":"Halim Z, Waqas M, Baig AR, Rashid A (2017) Efficient clustering of large uncertain graphs using neighborhood information. Int J Approx Reason 90:274\u2013291","journal-title":"Int J Approx Reason"},{"key":"4563_CR51","doi-asserted-by":"crossref","unstructured":"Jamil S, Khan A, Halim Z, Baig AR (2011) Weighted muse for frequent sub-graph pattern finding in uncertain DBLP data. In: 2011 international conference on internet technology and applications, IEEE, pp 1\u20136","DOI":"10.1109\/ITAP.2011.6006415"},{"key":"4563_CR52","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/S0020-0255(98)10066-X","volume":"113","author":"MS Sunitha","year":"1999","unstructured":"Sunitha MS, Vijayakumar A (1999) A characterization of fuzzy trees. Inf Sci 113:293\u2013300","journal-title":"Inf Sci"},{"key":"4563_CR53","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1186\/s40064-015-0935-5","volume":"4","author":"M Tom","year":"2015","unstructured":"Tom M, Sunitha MS (2015) Strong sum distance in fuzzy graphs. Springerplus 4:214. https:\/\/doi.org\/10.1186\/s40064-015-0935-5","journal-title":"Springerplus"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-019-04563-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-019-04563-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-019-04563-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,2]],"date-time":"2022-10-02T17:21:42Z","timestamp":1664731302000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-019-04563-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,24]]},"references-count":53,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["4563"],"URL":"https:\/\/doi.org\/10.1007\/s00521-019-04563-5","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,24]]},"assertion":[{"value":"4 February 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 October 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}