Physical Sciences and Mathematics Commons^™

Domination Number Of Annulus Triangulations, Toshiki Abe, Junki Higa, Shin-Ichi Tokunaga

Theory and Applications of Graphs

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.