Characterization of outerplanar graphs with equal 2-domination and domination numbers

Authors

Naoki Matsumoto, Keio UniversityFollow

Publication Date

July 2022

Abstract

A k-domination number of a graph G is minimum cardinality of a k-dominating set of G, where a subset S ⊆ V(G) is a k-dominating set if each vertex v ∈ V(G) \ S is adjacent to at least k vertices in S. It is known that for any graph G with Δ(G) ≥ k ≥ 2, γ_k(G) ≥ γ(G) + k – 2, and then γk(G) > γ(G) for any k ≥ 3, where γ(G) = γ1(G) is the usual domination number. Thus, it is the most interesting problem to characterize graphs G with γ2(G) = γ(G). In this paper, we characterize outerplanar graphs with equal 2-domination and domination numbers.

Creative Commons License

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

Recommended Citation

Matsumoto, Naoki (2022) "Characterization of outerplanar graphs with equal 2-domination and domination numbers," Theory and Applications of Graphs: Vol. 9: Iss. 2, Article 1.
DOI: 10.20429/tag.2022.090201
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol9/iss2/1