Polynomial solvability of the independent set problem for one class of graphs with small diameter

A constructive approach to forming new cases in the family of hereditary parts of the set ${\mathcal Free}(\{P_5,C_5\})$ with polynomial-time solvability of the independent set problem is considered. We prove that if this problem is polynomial-time solvable in the class ${\mathcal Free}(\{P_5,C_5,G\})$ then for any graph $H$ which can inductively be obtained from $G$ by means of applying addition with $K_1$ or multiplication by $K_1$ to the graph $G$ the problem has the same computational status in ${\mathcal Free}(\{P_5,C_5,H\})$. Bibliogr. 10.