Metric and partition dimension of flower and pencil graphs

نویسندگان
Wijaya, Kristiana ID 1
Abshari, Ulil ID 2
Halikin, Ikhsanul ID 3
Diniyah, Via Mufidatud ID 4
Kusbudiono, Kusbudiono ID 5

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

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

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

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

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

doi
10.22059/jac.2024.360428.1198
چکیده

This paper is about metric and partition dimension of a flower and a pencilgraph. A metric dimension of G, denoted by dim(G), is the minimum cardinality of anyresolving 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 themetric dimension of a flower graph fm×n for m ∈ {3, 4} and a pencil graph Pcm for anyinteger m ≥ 2. We also give the partition dimension of fm×n for m ∈ {3, 4, 5} and Pcmfor any integer m ≥ 2.

کلیدواژه‌ها
Distance, resolving set, resolving $k$-ordered partition, ordered $k$-tupple, connected