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All Journal Indonesian Journal of Combinatorics
Haryeni, Debi Oktia
Universitas Pertahanan Republik Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management

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Family of Graphs with Partition Dimension Three Haryeni, Debi Oktia; Baskoro, Edy Tri; Saputro, Suhadi Wido
Indonesian Journal of Combinatorics Vol 8, No 2 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.2.1

Abstract

The characterization of all connected graphs of order n ≥3 with partition dimension 2, n−1 or n has been completely done. Additionally, all connected graphs of order n≥9 with partition dimension n−2 and graphs of order n≥11 with partition dimension n−3 have been characterized as well. However, the characterization of all connected graphs with partition dimension 3 is an open problem. In this paper, we construct many families of disconnected as well as connected graphs with partition dimension 3 by generalizing the concept of the partition dimension so that it can be applied to disconnected graphs.
Co-Authors Baskoro, Edy Tri Saputro, Suhadi Wido