On the Locating Edge Domination Number of Comb Product of Graphs
Dafik Dafik, Ika Hesti Agustin, Moh. Hasan, Robiatul Adawiyah, Ridho Alfarisi, Dwi Agustin Retnowardani · Journal of Physics Conference Series · 2018
Let G = ( V, E ) be a graph. For e 1 ∈ E, N ( e 1 ) denote the neighborhoods of e 1 in G . A set D ⊆ E is a locating edge dominating set if every two distinct 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. The comb product between G and H , denoted by G ⊲ H , is a graph obtained by one copy of G and | V ( G )| copies of H , and grafting the i vertex of G to the u i in i -th copy of H . In this paper, we will analyze the locating edge dominating number of comb product of graphs and also find its best lower bound.