All Graphs of Order n with Distinguishing Number n−1 or n − 2

Authors

Andi Pujo Rahadi, Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, IndonesiaFollow
Edy Tri Baskoro, Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia, and Center for Research Collaboration on Graph Theory and CombinatoricsFollow
Suhadi Wido Saputro, Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, IndonesiaFollow

Abstract

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.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Rahadi, Andi Pujo; Baskoro, Edy Tri; and Saputro, Suhadi Wido (2025) "All Graphs of Order n with Distinguishing Number n−1 or n − 2," Theory and Applications of Graphs: Vol. 12: Iss. 1, Article 3.
DOI: 10.20429/tag.2025.120103
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol12/iss1/3