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Domination number of annulus triangulations
An {\em annulus triangulation} is a 2-connected plane graph with two disjoint faces and such that every face other than and are triangular, and that every vertex of is contained in the boundary cycle of or . In this paper, we prove that every annulus triangulation with vertices of degree 2 has a dominating set with cardinality at most if is not isomorphic to the octahedron. In particular, this bound is best possible