On the domination of triangulated discs

Abstract

. Let G be a 3-connected triangulated disc of order n with the boundary cycle C of the outer face of G . Tokunaga (2013) conjectured that G has a dominating set of cardinality at most 14 ( n +2). This conjecture is proved in Tokunaga (2020) for G − C being a tree. In this paper we prove the above conjecture for G − C being a unicyclic graph. We also deduce some bounds for the double domination number, total domination number and double total domination number in triangulated discs.