Locating fair domination in graphs.

Graphs considered here are simple, finite and undirected. A graph is denoted by G and its vertex set by V (G) and edge set by E (G). Many researchers were attracted by two concepts introduced in [P. J. Slater, Domination and location in acyclic graphs, Networks17 (1987) 55–64; P. J. Slater, Dominating and reference sets in graphs, J. Math. Phys. Sci. 22 (1988) 445–455; Y. Caro, A. Hansberg and M. Henning, Fair domination in graphs, Discrete Math. 312 (2012) 2905–2914]. One is locating domination and the other is fair domination. A subset D of V (G) is called a locating dominating set of G if for any u , v ∈ V − D , N (u) ∩ D ≠ N (v) ∩ D and both sets are non-empty. D is called a fair dominating set of G for any u , v ∈ D , | N (u) ∩ D | = | N (v) ∩ D | > 0. In this paper, both properties are combined and locating fair domination is studied. [ABSTRACT FROM AUTHOR]