(untitled) (International Journal of Food and Nutritional Sciences, 2022)
The tensor product ????1 ⊗ ????2 of two graphs ????1 = (????1, ????1) and ????2 = (????2, ????2) such that the vertex set of ????1 × ????2 is the cartesian product ????(????1) × ????(????2) and two vertices sets (???????? , ???????? ) and (???????? , ????????), ????, ????, ????, ???? = 1, 2, …. in ????(????1) × ????(????2) are adjacent, if ???????????????? ∈ ????1 and ???????????????? ∈ ????2 the tensor product ????1 ⊗ ????2 it is denoted by ????(????1 ⊗ ????2). A set ???? of vertices of a graph ????(????1 ⊗ ????2) is locating, if any two distinct vertices sets (????????, ???????? ), (????????, ???????? ) outside ????, ????(????????, ????????) ∩ ???? ≠ ????(????????, ???????? ) ∩ ????, where ????(????????, ????????), ????(????????, ???????? ) denotes the open neighborhood of (???????? , ????????) and (???????? , ????????). If ???? is also a dominating set, it is called a locating set of ????(????1 ⊗ ????2) and denoted by ????????????(????(????1 ⊗ ????2)). In this paper, we establish a locating domination number of tensor product ????1 ⊗ ????2 graph. Further, we also discuss path, cycle, star, complete graph and properties of ????(????1 ⊗ ????2).