Rini Anggriani, Tjang Daniel Chandra, Desi Rahmadani
Let G be a connected and simple graph and Li ⊆ V(G) for all i = 1, 2,, k. For an ordered k - partition ∏={L1,L2,L3,..,Lk} of V(G) and a vertex v ∈ V(G). The representation of v with respect to Π is defined as the k-vector r(v|∏)=(d(v,L1), d(v,L2), d(v,L3),..,d(v,Lk)). If r(u|∏)≠r(v|∏), for every vertex in u, v ∈ V(G), then the k-partition Π is called a resolving partition of V(G). The minimum k such that Ghas a resolving k - partition of V(G) is the partition dimension of G, denoted by pd(G). In this paper, we will determine the partition dimension of the sunlet graph S3k, for k ≥ 1 and an upper bound for the partition dimension of amalgamation of the sunlet graphs Amal(S3)m, for any m ≥ 2. © 2024 Author(s).
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang, Malang, Indonesia
