A hypergraph is a generalization of a graph where edges can connect any number of vertices. In this paper, we extend the study of locating-dominating sets to hypergraphs. Along with some basic results, sharp bounds for the locationdomination number of hypergraphs in general and exact values with specified conditions are investigated. Moreover, locating-dominating sets in some specific hypergraphs are found. -complete problem [8]. In [6], it was pointed out that each locating-dominating set is both the locating and dominating set. However, a set that is both the locating and dominating is not necessarily a locating-dominating set.
NPA hypergraph H is a pair (V (H), E(H)), where V (H) is a finite set of vertices and E(H) is a finite family of non-empty subsets of V (H), called hyperedges, withso in a linear hypergraph, there may be no repeated hyperedges of cardinality greater than one. A hypergraph H with no hyperedge is a subset of any other hyperedge is called Sperner.AIf v is incident with exactly n hyperedges, then we say that the degree of v is n; if all the vertices v ∈ V (H) have degree n, then H is n-regular. The maximum degree of any vertex in H is denoted by ∆(H). Similarly, if there are exactly n vertices incident with a hyperedge E, then we say that the size of E is n; if all the hyperedges E ∈ E(H) have size n, then H is n-uniform. A simple graph is a 2-uniform hypergraph.A path from a vertex v to another vertex u, in a hypergraph, is a finite sequence of the form v, , having length l such that v ∈ E 1 , w i ∈ E i ∩ E i+1 for i = 1, 2, . . . , l − 1 and u ∈ E l . A hypergraph H is connected if there is a path between every two vertices of H. All the hypergraphs considered in this paper are connected Sperner hypergraphs.A hypergraph H is said to be a hyperstar if E i ∩E j = C = ∅, for any E i , E j ∈ E(H). We will call C, the center of the hyperstar. If there exists a sequence of hyperedges E 1 , E 2 , . . . , E k in a hypergraph H, then H is said to be (1) a hyperpath if E i ∩E j = ∅ if and only if |i − j| = 1; (2) a hypercycle if E i ∩ E j = ∅ if and only if |i − j| = 1 (mod k). A connected hypergraph H with no hypercycle is called a hypertree.In graphs, the theory of dominating sets and locating-dominating sets is extensively studied. Hypergraphs, in the context of domination, were firstly considered by Behr and Camarinopoulos in 1998 [4], and further considered by Acharya [1,2] and Jose and Tuza [13]. In this paper, we consider hypergraphs in the context of location-domination. We give some sharp lower bounds for the location-domination number of hypergraphs. Also, we investigate the location-domination number of some well-known families of hypergraphs such as hyperpaths, hypercycles and kpartite hypergraphs.
Some Basic Results and BoundsTwo vertices u and v of a hypergraph incident with the same hyperedge are said to be coincident vertices. Let E (d) i = {E i 1 , E i 2 , . . . , E i d } be a collection of hyperedges.
