Domination number of annulus triangulations

Authors

Toshiki Abe, Yokohama National UniversityFollow
Junki HigaFollow
Shin-ichi Tokunaga, Tokyo Medical and Dental UniversityFollow

Abstract

An annulus triangulation G is a 2-connected plane graph with two disjoint faces f₁ and f₂ such that every face other than f₁ and f₂ are triangular, and that every vertex of G is contained in the boundary cycle of f₁ or f₂. In this paper, we prove that every annulus triangulation G with t vertices of degree 2 has a dominating set with cardinality at most ⌊ \frac{|V(G)|+t+1}{4} ⌋ if G is not isomorphic to the octahedron. In particular, this bound is best possible.

Creative Commons License

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

Recommended Citation

Abe, Toshiki; Higa, Junki; and Tokunaga, Shin-ichi (2020) "Domination number of annulus triangulations," Theory and Applications of Graphs: Vol. 7: Iss. 1, Article 6.
DOI: 10.20429/tag.2020.070106
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol7/iss1/6