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

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