Location detection is studied for many scenarios, such as pointing out the flaws in multiprocessors, invaders buildings and facilities, utilizing wireless sensor networks monitoring environmental processes. The system or structure can be illustrated a graph each of these applications. Sensors strategically placed at subset vertices determine identify irregularities within network. open locating...

A set D of vertices of a graph G is locating if every two distinct vertices outside D have distinct neighbors in D; that is, for distinct vertices u and v outside D, N(u) ∩ D ≠ N(v) ∩ D, where N(u) denotes the open neighborhood of u. If D is also a dominating set (total dominating set), it is called a locating-dominating set (respectively, locating-total dominating set) of G. A graph G is twin-...

Let c be a proper k-coloring of a connected graph G andΠ = (C1, C2, . . . , Ck) be an ordered partition of V (G) into the resulting color classes. For a vertex v of G, the color code of v with respect to Π is defined to be the ordered k-tuple c Π (v) := (d(v, C1), d(v, C2), . . . , d(v, Ck)), where d(v, Ci) = min{d(v, x)|x ∈ Ci}, 1 ≤ i ≤ k. If distinct vertices have distinct color codes, then c...

A set S ⊆ V (G) of an undirected graph G is a locating-dominating if for each v ∈ \ S, there exists w such tha vw E(G) and NG(x) ∩ ̸= NG(y) any two distinct vertices x y in S. stable it {v} The minimum cardinality G, denoted by γSLD(G), called the locating-domination number G. In this paper, we investigate concept corresponding parameter edge corona lexicographic product graphs.