All Graphs of Order n with Distinguishing Number n−1 or n − 2
Let G be a simple connected graph. The distinguishing number of G, denoted by D(G), is the least integer d such that G has a vertex d-labeling preserved only by the trivial automorphism. In this paper, we characterize all graphs of order n with distinguishing number n − 1, or n − 2.
Authors
- Suhadi Wido Saputro (ORCID: https://orcid.org/0000-0003-3886-400X)
- Edy Tri Baskoro (ORCID: https://orcid.org/0000-0003-0492-5142)
- Andi Pujo Rahadi (ORCID: https://orcid.org/0000-0002-6532-3017)
Publication Details
- Journal
- Theory and Applications of Graphs
- Published
- 2025-01-01
- DOI
- https://doi.org/10.20429/tag.2025.120103
- Primary Topic
- Graph Labeling and Dimension Problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00