Proceedings of the SEMANTIK Conference of Mathematics Education (SEMANTIK 2019)

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
https://doi.org/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/).

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Volume Title
Proceedings of the SEMANTIK Conference of Mathematics Education (SEMANTIK 2019)
Series
Advances in Social Science, Education and Humanities Research
Publication Date
28 August 2020
ISBN
978-94-6239-049-2
ISSN
2352-5398
DOI
https://doi.org/10.2991/assehr.k.200827.113How to use a DOI?
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  - https://doi.org/10.2991/assehr.k.200827.113
ID  - Hidayah2020
ER  -