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Article Title
Abstract
An {\em annulus triangulation} $G$ is a 2-connected plane graph with two disjoint faces $f_1$ and $f_2$ such that every face other than $f_1$ and $f_2$ are triangular, and that every vertex of $G$ is contained in the boundary cycle of $f_1$ or $f_2$. In this paper, we prove that every annulus triangulation $G$ with $t$ vertices of degree 2 has a dominating set with cardinality at most $\lfloor \frac{|V(G)|+t+1}{4} \rfloor$ if $G$ is not isomorphic to the octahedron. In particular, this bound is best possible.
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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