Portal de Periódicos da CAPES

On the local multiset dimension of m -shadow graph

2019; IOP Publishing; Volume: 1211; Linguagem: Inglês

10.1088/1742-6596/1211/1/012006

1742-6596

Robiatul Adawiyah, Dafik Dafik, Ika Hesti Agustin, Rafiantika Megahnia Prihandini, Ridho Alfarisi, E R Albirri,

Graph theory and applications

Let G = (V, E) be a simple and connected graph with edge set E and vertex set V . Suppose W = {s1, s2, ..., sk} is a subset of vertex set V (G), the representation multiset of a vertex v of G with respect to W is where d(v, si) is a distance between v and the vertices in W together with their multiplicities. The resolving set W is a local resolving set of G if for every pair u, v of adjacent vertices of a graph G. The minimum local resolving set W is a local multiset basis of G. If G has a local multiset basis, then its cardinality is called local multiset dimension, denoted by µl(G). In this paper, we analyzed the local multiset dimension of m-shadow graph. The m − shadow of a connected graph G, denoted by Dm(G), is constructed by taking m copies of G, say then join each vertex u in Gi to the neighbors of the corresponding vertex v in Gj, where 1 ≤ i and j ≤ m. We will investigate the characterization and exact value of local multiset dimension of m-shadowing of cycle graph, m-shadowing of star graph, m-shadowing of path graph, and m-shadowing of complete graph.