Independent transversal dominating sets in graphs: Complexity and structural properties
Hossein Ahangar Abdollahzadeh, Vladimir Samodivkin, Ismael G. Yero · Filomat · 2016
A dominating set of a graph G which intersects every independent set of maximum cardinality in G is called an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of G and is denoted by γit(G). In this paper we study some complexity issues on some independent transversal domination related problems. On the other side, we prove that for every integers a, b, c with a ≤ b ≤ a + c, there exists a graph G such that G has domination number a, minimum degree c and independent transversal domination number b. We also give some other properties of independent transversal dominating sets in graphs.