Related Wheel Graphs and Its Locating Edge Domination Number
Robiatul Adawiyah, Ika Hesti Agustin, Dafik Dafik, Slamin Slamin, Ermita Rizki Albirri · Journal of Physics Conference Series · 2018
A subset D of E ( G ) is called an edge dominating set of G if every edge not in D is adjacent to some edges in D . In this paper, we initiate to study a new concept in edge dominating set. It is locating edge dominating set. A set D ⊆ E is a locating edge dominating set if every two edges e 1 , e 2 ∈ E ( G )\ D satisfy that Ø ≠ N ( e 1 ) ∩ D ≠ N ( e 2 ) ∩ D ≠ ø. The locating edge domination number is the minimum cardinality of locating edge dominating set. In this research, we analyze the locating edge domination number of some related wheel graphs. We also analyze the upper bound of locating edge domination number.