The local metric dimension of split and unicyclic graphs
Abstrak
A set <em>W</em> is called a local resolving set of <em>G</em> if the distance of <em>u</em> and <em>v</em> to some elements of <em>W</em> are distinct for every two adjacent vertices <em>u</em> and <em>v</em> in <em>G</em>. The local metric dimension of <em>G</em> is the minimum cardinality of a local resolving set of <em>G</em>. A connected graph <em>G</em> is called a split graph if <em>V</em>(<em>G</em>) can be partitioned into two subsets <em>V</em><sub>1</sub> and <em>V</em><sub>2</sub> where an induced subgraph of G by <em>V</em><sub>1</sub> and <em>V</em><sub>2</sub> is a complete graph and an independent set, respectively. We also consider a graph, namely the unicyclic graph which is a connected graph containing exactly one cycle. In this paper, we provide a general sharp bounds of local metric dimension of split graph. We also determine an exact value of local metric dimension of any unicyclic graphs.
Topik & Kata Kunci
Penulis (4)
Dinny Fitriani
Anisa Rarasati
Suhadi Wido Saputro
Edy Tri Baskoro
Akses Cepat
- Tahun Terbit
- 2022
- Sumber Database
- DOAJ
- DOI
- 10.19184/ijc.2022.6.1.3
- Akses
- Open Access ✓