# k-Metric Dimension of Generalized Fan Graph and Cm ∗2 Kn Graph

Authors

Nur Hidayah, Tri Atmojo Kusmayadi

Corresponding Author

Nur Hidayah

Available Online 28 August 2020.

- DOI
- 10.2991/assehr.k.200827.113How to use a DOI?
- Keywords
- k-metric dimension, k-metric generator, basis of k-metric, generalized fan Fm, n graph, Cm *2 Kn graph
- Abstract
Let G be a simple connected graph with the vertex set V(G) and the set edge E(G). The set S ⊆ V(G) is called the k-metric generator on G if and only if every two different vertices in G are distinguished by at least k elements in S, in other words for every two different vertices u,v ∈ V(G), there are at least k vertices w1,w2,…,wk ∈ S such that d(u,wi) ≠ d(v,wi), for every i ∈ {1,…,k}. The k-metric generator with the smallest cardinality is called the k-metric base and the cardinality of the k-metric base is on call the k-metric dimension of the graph G denoted dimk(G). In this study, the k-metric dimension was obtained in generalized fan Fm,n graph with m ≥ 1, n ≥ 3 and Cm ∗2 Kn graph with m ≥ 3, n ≥ 2.

- Copyright
- © 2020, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

### Cite this article

TY - CONF AU - Nur Hidayah AU - Tri Atmojo Kusmayadi PY - 2020 DA - 2020/08/28 TI - k-Metric Dimension of Generalized Fan Graph and Cm ∗2 Kn Graph BT - Proceedings of the SEMANTIK Conference of Mathematics Education (SEMANTIK 2019) PB - Atlantis Press SP - 34 EP - 38 SN - 2352-5398 UR - https://doi.org/10.2991/assehr.k.200827.113 DO - 10.2991/assehr.k.200827.113 ID - Hidayah2020 ER -