All graphs of order n ≥ 11 and diameter 2 with partition dimension n - 3

Edy Tri Baskoro; Debi Oktia Haryeni

doi:10.1016/j.heliyon.2020.e03694

All graphs of order n ≥ 11 and diameter 2 with partition dimension n - 3

Heliyon. 2020 Apr 14;6(4):e03694. doi: 10.1016/j.heliyon.2020.e03694. eCollection 2020 Apr.

Authors

Edy Tri Baskoro¹, Debi Oktia Haryeni¹

Affiliation

¹ Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia.

Abstract

All graphs of order n with partition dimension 2, $n - 2$ , $n - 1$ , or n have been characterized. However, finding all graphs on n vertices with partition dimension other than these above numbers is still open. In this paper, we characterize all graphs of order $n \geq 11$ and diameter 2 with partition dimension $n - 3$ .

Keywords: Characterization; Diameter; Graph; Mathematics; Partition dimension.