For a graph G, we denote by c(G) the circumference of G, and let σ(G)=min{sum from i=1 to 3 d(v):{v, v, v} is an independent set in G},(G)=min{sum from i=1 to 3 d(v)-|N(v)|:{v, v, v} is an independent set in G}, ρ(G)=min{|N(v)|:{v, v, v} is an independent set in G} and