Metric Dimension dan Non-Isolated Resolving Number pada Beberapa Graf

Abstract

Let G = (V, E) be a set of ordered set W = {W1, W2, W3, ..., Wk} from the set of vertices in connected graph G. The metric dimension is the minimum cardinality of the resolving set on G. The representation of v on W is k set. Vector r(v|W) = (d(v, W1), d(v, W2), ..., d(v, Wk)) where d(x, y) is the distance between the vertices x and y. This study aims to determine the value of the metric dimensions and dimension of non-isolated resolving set on the wheel graph (Wn). Results of this study shows that for n ≥ 7, the value of the metric dimension and non-isolated resolving set wheel graph (Wn) is dim(Wn) = b n−1 2 c and nr(Wn) = b n+1 2 c. The first step is to determine the cardinality vertices and edges on the wheel graph, then determine W, with W is the resolving set G if vertices G has a different representation. Next determine non-isolated resolving set, where W on the wheel graph must have different representations of W and all x elements W is connected in W.