On the Locating Edge Domination Number of Comb Product of Graphs

Let G = (V, E) be a graph. For e1 ∈ E, N (e1) denote the neighborhoods of e1 in G. A set D ⊆ E is a locating edge dominating set if every two distinct edges e1, e2 ∈ E(G) \ D satisfy that Ø ≠ N(e1) ∩ D ≠ N(e2) ∩ D ≠ Ø. The locating edge domination number γL′(G) is the minimum cardinality of locating...

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Bibliographic Details
Published in:Journal of physics. Conference series 2018-05, Vol.1022 (1), p.12003
Main Authors: Dafik, Agustin, I. H., Hasan, Moh, Adawiyah, R., Alfarisi, R., Wardani, D.A.R.
Format: Article
Language:English
Subjects:
comb product of graphs
Graphs
Locating edge dominating set
locating edge domination number
Lower bounds
Physics
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Summary:Let G = (V, E) be a graph. For e1 ∈ E, N (e1) denote the neighborhoods of e1 in G. A set D ⊆ E is a locating edge dominating set if every two distinct edges e1, e2 ∈ E(G) \ D satisfy that Ø ≠ N(e1) ∩ D ≠ N(e2) ∩ D ≠ Ø. The locating edge domination number γL′(G) 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 ui 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.
ISSN:1742-6588
1742-6596
1742-6596
DOI:10.1088/1742-6596/1022/1/012003