Connected Dominating Sets in Graphs With Stability Number Three

Abstract

In the special case of graphs G of independence number a(G)=3 without induced chordless cycles C7 it is shown that exists connected dominating set D of vertices with number of vertices n(D)<=4. Using the concept of connected dominating sets, we defined a new invariant h(G) that does not exceed the number of Hadwiger. For the considered graphs it is shown that h(G)>=n(G)/4.