Connected Domination Number and a New Invariant in Graphs with Independence Number Three

摘要

Adding a connected dominating set of vertices to a graph G increases its number of Hadwiger h(G). Based on this obvious property in [2] we introduced a new invariant eta(G) for which eta(G) = h(G). We continue to study its property. For a graph G with independence number three without induced chordless cycles C-7 and with n(G) vertices, eta(G) = n(G)/4.