Indonesian Journal of Combinatorics
Vol 8, No 2 (2024)

Family of Graphs with Partition Dimension Three

Haryeni, Debi Oktia (Universitas Pertahanan Republik Indonesia)
Baskoro, Edy Tri (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)
Saputro, Suhadi Wido (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)

Article Info

Publish Date
31 Dec 2024

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.

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Journal Info
Indonesian Journal of Combinatorics
Website

Abbrev

ijc

Publisher

Indonesian Combinatorial Society

Subject

Computer Science & IT Decision Sciences, Operations Research & Management

Description

Indonesian Journal of Combinatorics (IJC) publishes current research articles in any area of combinatorics and graph theory such as graph labelings, optimal network problems, metric dimension, graph coloring, rainbow connection and other related topics. IJC is published by the Indonesian ...