The dominating partition dimension and locating-chromatic number of graphs
| Main Authors: | Ridwan, Muhammad; Institut Teknologi Bandung, Assiyatun, Hilda; Institut Teknologi Bandung, Baskoro, Edy Tri; Institut Teknologi Bandung |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2023
|
| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1684 https://www.ejgta.org/index.php/ejgta/article/view/1684/pdf_281 https://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/1684/311 |
Daftar Isi:
- For every graph G, the dominating partition dimension of G is either the same as its partition dimension or one higher than its partition dimension. In this paper, we consider some general connections among these three graph parameters: partition dimension, locating-chromatic number, and dominating partition dimension. We will show that βp(G)≤ηp(G)≤χL(G) for any graph G with at least 3 vertices. Therefore, we will derive properties for which graphs G have ηp(G)=βp(G) or ηp(G)=βp(G)+1.