THE LOCATING-DOMINATING NUMBER OF GENERALIZED FAN GRAPHS

• Main Author: SULASTRI LUBIS (NIM: 90113009), SUSI
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/20561
• Institution: Institut Teknologi Bandung

Let G = (V,E) be a connected simple graph with the vertex set V and the edge set E. The set W ⊆ V (G) is a locating-dominating set of G if every two different vertices u,v ∈ V (G)W satisfies ∅6= N(u)∩W 6= N(v)∩W 6= ∅. The minimum cardinality of a locating-dominating set of G is called locating-dominating number of G, denoted by λ(G). In this project, we determine the locating-dominating number of a fan graphs F1,n and a generalized fan graphs GF (F1,n1,F1,n2,...,F1,nk). The fan graph F1,n is a graph obtained from a path of n vertices and one additional vertex V such that every vertex of a path is adjacent to v. The generalized fan graph GF (F1,n1,F1,n2,...,F1,nk) is a graph obtained from fan graphs F1,n1,F1,n2,...,F1,nk where ni ≥ 3 by identificate all fan graphs in their center vertex.