## Metric Dimension dan Non-Isolated Resolving Number pada Beberapa Graf

##### Date

2021-06-01##### Author

SHOLIHAH, Wahyu Nikmatus

DAFIK, Dafik

KUSBUDIONO, Kusbudiono

##### Metadata

Show full item record##### 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.

##### Collections

- LSP-Jurnal Ilmiah Dosen [7287]

UPA-TIK Copyright © 2024 Library University of Jember