In[1]

it is shown that every quadrangularly connected claw-free graph G without vertices of degree 1

which does not contain an induced subgraph H isomorphic to either G1 or G2(see Fig.1.) such that N1(x

G) of every vertex x of degree 4 in H is disconnected is hamiltonian.However

in[2]

there are some flaws in the statements and the proofs of Proposition 2.5 and Theorem 2.6.In this note

we restate them in a correct form and give modified proofs.