{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T19:15:38Z","timestamp":1769714138269,"version":"3.49.0"},"reference-count":50,"publisher":"SAGE Publications","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,8,1]]},"abstract":"<jats:p>\u00a0Let N\u00a0=\u00a0(V, E) be a simple graph and let X be a subset of V\u00a0(N). If every node not in X lies on a geodesic path between two nodes from X then it is called a geodetic set. The geodetic number g\u00a0(N) is the minimum cardinality of such set X. The subset X is called a dominating set if every node not in X has at least one neighbour in X. The minimum number of nodes of a dominating set is known as domination number \u03b3\u00a0(N). If the subset X is a geodetic set as well as a dominating set then it is called a geodetic dominating set. The minimum cardinality of a geodetic dominating set is known as geodetic domination number \u03b3g\u00a0(N). The geodetic domination integrity of N is defined to be DIg\u00a0(N)\u00a0=\u00a0min\u00a0{|X|\u00a0+\u00a0m\u00a0(N\u00a0-\u00a0X)\u00a0:\u00a0X is a geodetic dominating set of N}, where m\u00a0(N\u00a0-\u00a0X) denotes the order of the largest component of N\u00a0-\u00a0X. Uncertain networks can be modelled using fuzzy graphs. In a graph, each vertex and each edge are equally significant. However, in fuzzy graphs, each vertex and each edge is important in terms of fuzziness in their own right. In this study, the concepts of geodetic dominating sets in fuzzy graphs and geodetic domination number are defined and bounds are obtained. Moreover, the vulnerability parameter Geodetic domination integrity is introduced in fuzzy graphs. Further, the geodetic domination integrity for complete fuzzy graphs, complete bipartite fuzzy graphs, Cartesian product of two strong fuzzy graphs and bounds are also discussed. The applications of this parameter are applied to a telecommunication network system model to identify the key persons in the system and applied in a fuzzy social network to find the most influential group within the network.<\/jats:p>","DOI":"10.3233\/jifs-223249","type":"journal-article","created":{"date-parts":[[2023,5,19]],"date-time":"2023-05-19T12:23:27Z","timestamp":1684499007000},"page":"2209-2222","source":"Crossref","is-referenced-by-count":0,"title":["Geodetic domination integrity in fuzzy graphs"],"prefix":"10.1177","volume":"45","author":[{"given":"Balaraman","family":"Ganesan","sequence":"first","affiliation":[{"name":"Department of Mathematics, St. Joseph\u2019s Instituteof Technology, OMR, Chennai, Tamilnadu, India"}]},{"given":"Sundareswaran","family":"Raman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, OMR, Chennai, Tamilnadu, India"}]},{"given":"Shanmugapriya","family":"Marayanagaraj","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, OMR, Chennai, Tamilnadu, India"}]},{"given":"Said","family":"Broumi","sequence":"additional","affiliation":[{"name":"Laboratory of Information Processing, Faculty of Science Ben M\u2019Sik, University of Hassan II, Casablanca, Morocco"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-223249_ref2","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/S0020-0255(02)00411-5","article-title":"Strong arcs in fuzzy graphs","volume":"152","author":"Bhutani","year":"2003","journal-title":"Inform Sci"},{"key":"10.3233\/JIFS-223249_ref3","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0020-0255(94)90116-3","article-title":"Operations on fuzzy graphs","volume":"79","author":"Mordeson","year":"1994","journal-title":"Inform Sci"},{"issue":"2","key":"10.3233\/JIFS-223249_ref4","first-page":"363","article-title":"Domination in interval-valued fuzzy graphs","volume":"6","author":"Debnath","year":"2013","journal-title":"Ann Fuzzy Math Inform"},{"issue":"1","key":"10.3233\/JIFS-223249_ref5","first-page":"47","article-title":"Isomorphism on interval valued fuzzy graphs","volume":"6","author":"Talebi","year":"2013","journal-title":"Ann Fuzzy Math Inform"},{"key":"10.3233\/JIFS-223249_ref6","doi-asserted-by":"crossref","unstructured":"Yeh R.T. and Bang S.Y. , Fuzzy relations, fuzzy graphs and their applications to clustering analysis, in: L.A. 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