he condition for Theorem 2 presented in Ref.[1] is relaxed in this paper wherein itis also indicated that the condition“3-degree sum”can be reduced to any three independent ver-tices x,y and z that meet min{d(x,y),d(y,z),d(z,x)}=2 in a n-order graph,leading todd(x)+d(y>)+d(z)≥n. Corresponding results will hold under this condition.