Journal of Algorithms and Computation
Open Access

Metric and partition dimension of flower and pencil graphs

Document Type : Research Paper

Authors

Kristiana Wijaya
Ulil Abshari
Via Mufidatud Diniyah
Ikhsanul Halikin
Kusbudiono Kusbudiono

Graph and Algebra Research Group Department of Mathematics Faculty of MIPA Universitas Jember

https://doi.org/10.22059/jac.2024.360428.1198
Abstract
This paper is about metric and partition dimension of a flower and a pencil

graph. A metric dimension of G, denoted by dim(G), is the minimum cardinality of any

resolving set of G. A partition dimension of G, denoted by pd(G), is the minimum number of sets in any resolving k-ordered partition for G. Here we give the exact value of the

metric dimension of a flower graph fm×n for m ∈ {3, 4} and a pencil graph Pcm for any

integer m ≥ 2. We also give the partition dimension of fm×n for m ∈ {3, 4, 5} and Pcm

for any integer m ≥ 2.

Keywords

Distance
resolving set
resolving $k$-ordered partition
ordered $k$-tupple
connected
Journal of Algorithms and Computation
Volume 56, Issue 1
August 2024
Pages 83-99

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