BI-DIMENSI METRIK DARI GRAF ANTIPRISMA

Abstract

Let G = (V, E) be a simple and connected graph. For each x ∈ V(G), it is associated with a vector pair (a, b), denoted by S x , corresponding to subset S = {s1 , s2 , ... , s k } ⊆ V(G), with a = (d(x, s₁ ), d(x, s₂ ), ... , d(x, s _k )) and b = (δ(x, s₁ ), δ(x, s₂ ), ... , δ(x, s _k )). d(v, s) is the length of shortest path from vertex v to s, and δ(v, s) is the length of the furthest path from vertex v to s. The set S is called the bi-resolving set in G if S _x ≠ S _y for any two distinct vertices x, y ∈ V(G). The bi- metric dimension of graph G, denoted by β _b (G), is the minimum cardinality of the bi-resolving set in graph G. In this study we analyze bi-metric dimension in the antiprism graph (A _n ). From the analysis that has been done, it is obtained the result that bi-metric dimension of graph A _n , β _b (A _n ) is 3.
Keywords: Antiprism graph, bi-metric dimension, bi-resolving set. .