Locating fair domination in graphs

V Swaminathan, R Sundareswaran… - Discrete Mathematics …, 2024 - World Scientific
V Swaminathan, R Sundareswaran, L Muthusubramanian
Discrete Mathematics, Algorithms and Applications, 2024World Scientific
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 [PJ Slater, Domination and location in acyclic graphs, Networks 17 (1987) 55–
64; PJ 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 …
Graphs considered here are simple, finite and undirected. A graph is denoted by and its vertex set by and edge set by . Many researchers were attracted by two concepts introduced in [P. J. Slater, Domination and location in acyclic graphs, Networks 17 (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 of is called a locating dominating set of if for any and both sets are non-empty. is called a fair dominating set of for any . In this paper, both properties are combined and locating fair domination is studied.
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