Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource PHD PhD PhD Thesis Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Relation A related resource 61000226 Title A name given to the resource A Study on Restrained Geodetic Domination in Graphs Subject The topic of the resource Mathematics and Statistics Description An account of the resource In a graph G = (V, E), the shortest path between any two vertices u and v in G is u and#8722; v geodesic. This distance concept leads to the introduction of geodetic set and geodetic number which has wide applications in location theory and convexity theory. A vertex subset S of a graph G is said to be a geodetic set, if all vertex in G is in u and#8722; v geodesic for some pair of vertices u and v in S. The minimum cardinality of such a set is the geodetic number and is denoted as g(G). A vertex subset M of a graph G is said to be a dominating set of G if for all vertex v and#8712; V (G), either v and#8712; M or v is adjacent to a vertex in M. The minimum cardinality of such a set is the domination number and is denoted by and#947;(G). In general, the geodetic set and newlinethe dominating set of a graph need not be the same. This led to the study of the geodetic dominating set. If a geodetic set S is a dominating set of a graph G, then S is called a geodetic dominating set. The minimum cardinality of such a set is the geodetic domination number, which is represented by and#947;g(G). There are several studies done on the geodetic and domination concepts so far. In the present study, we have explored the concept of restrained geodetic domination and its structural properties in graphs particularly in product graphs and derived graphs. A vertex subset S of a graph G = (V, E) is called a restrained geodetic dominating set if S is a geodetic dominating set of G and lt V and#8722; S gt has no isolated vertex. The minimum cardinality of such a set is called restrained geodetic domination number, which is denoted by and#947;gr(G). We have studied this concept for diand#64256;erent classes of graphs and concerning the graph operations such as Cartesian product, corona product, and join of graphs. Further, the study is extended to restrained geodetic domination in derived graphs such as edge subdivision graph, line graph and power of a graph. Also, investigated the properties of graphs with the restrained geodetic domination number equal to the order of the graph. Creator An entity primarily responsible for making the resource Joy, John. Source A related resource from which the described resource is derived Author's Submission Publisher An entity responsible for making the resource available Christ(Deemed to be University) Date A point or period of time associated with an event in the lifecycle of the resource 2023-01-01 Contributor An entity responsible for making contributions to the resource Shathish, Sangeetha. Rights Information about rights held in and over the resource Open Access Format The file format, physical medium, or dimensions of the resource PDF Language A language of the resource English Type The nature or genre of the resource PhD Identifier An unambiguous reference to the resource within a given context <a href="http://hdl.handle.net/10603/492346" target="_blank" rel="noreferrer noopener">http://hdl.handle.net/10603/492346</a>