Dominant Local Metric Dimension of Wheel Related Graphs
Reni Umilasari, Liliek Susilowati, Slamin Slamin · IOP Conference Series Materials Science and Engineering · 2021
Abstract Dominant local metric dimension is consist of two interesting topic in graph theory, they are dominating and metric dimension which be expanded as local metric dimension. A graph G is said having dominant local metric dimension if G be a connected graph and there is an ordered subset W l = {W 1, W 2 …, W n }⊆V(G) where W l is a local resolving set as well as a dominating set of G. Minimum cardinality of dominant local resolving set of G is called the dominant local basis of G. Then, cardinality of the dominant local basis of G is called the dominant local metric dimension of G which denoted by Ddim l (G). In this paper, we determine the dominant local metric dimension of wheel related graphs. That are Wheel, Jahangir, Friendship and Helm graph. Furthermore, we characterize the dominant local metric dimension of those graphs.