All graphs of order n ≥ 11 and diameter 2 with partition dimension n − 3
Edy Tri Baskoro,
Debi Oktia Haryeni
Affiliations
Edy Tri Baskoro
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia
Debi Oktia Haryeni
Corresponding author.; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia
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≥11 and diameter 2 with partition dimension n−3.
