Open Access
Research Article
On the partition dimension of directed circulant graphs
Elizabeth C. M. MaritzDepartment of Mathematics and Applied MathematicsBloemfontein 9300University of the Free StateP. O. Box 339, South AfricaView full profile → , *Tomáš VetríkCorresponding authorvetrikt@ufs.ac.zaDepartment of Mathematics and Applied MathematicsBloemfontein 9300University of the Free StateP. O. Box 339, South AfricaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 31 May 2019
- Published Online:
- 04 Feb 2021
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-943
- Pages:
- 1–10
Abstract
The directed circulant graph Cn(1, 2, … , t) consists of the vertices v0 , v1 , … , vn-1 and edges directed from vi to vi+j for every i = 0, 1, … , n – 1, and j = 1, 2, … , t, where 1 ≤ t ≤ n – 1, the indices are taken modulo n. We present lower and upper bounds on the partition dimension of very general graphs Cn(1, 2, … , t). Our bounds yield exact values of the partition dimension of the graphs Cn(1, 2, … , t) for t = 2, 3, 4 and n ≥ 10.
Keywords
Subject Classifications
(2010) 05C3505C12
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