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Wahyu Nikmatus Sholihah
Universitas Jember
Computer Science & IT Other

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Metric Dimension dan Non-Isolated Resolving Number pada Beberapa Graf Wahyu Nikmatus Sholihah; Dafik Dafik; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (372.906 KB) | DOI: 10.25037/cgantjma.v2i1.48

Abstract

Let $G=(V, E)$ be a set of ordered set $W=\{W_1,W_2, W_3,...,W_k\}$ 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 $r(v|W)=(d(v, W_1), d(v, W_2), ...,$ $d(v, W_k))$ 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 {\it non-isolated resolving set} on the wheel graph $(W_n)$. Results of this study shows that for $n \geq 7$, the value of the metric dimension and {\it non-isolated resolving set} wheel graph $(W_n)$ is $dim(W_n)=\lfloor \frac{n-1}{2} \rfloor$ and $nr(W_n)=\lfloor \frac{n+1}{2}\rfloor$. 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 {\it vertices} $G$ has a different representation. Next determine {\it non-isolated resolving set}, where $W$ on the wheel graph must have different representations of $W$ and all $x$ elements $W$ is connected in $W$. 
Co-Authors D. Dafik Kusbudiono Kusbudiono, Kusbudiono