For non-negative integers i, j and k, we denote the generalized net as Ni,j,k, which is a triangle with disjoint paths of length i, j and k, attached to distinct vertices of the triangle. In this paper, we prove that every 3-connected {K1,3,N8−i,i,1}-free graph is hamiltonian, where 1 ≤ i ≤ 4. © 2016, Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of ...