EIGENVALUES AND HAMILTONICITY OF QUASI - CLAW - FREE GRAPHS

A graph is quasi - claw - free if it satisfies the property: d(x, y) = 2 ⇒ there exists u ∈ N(x)∩N(y) such that N[u] ⊆ N[x]∪[N[y]. Let G be a k - connected quasi - claw - free graph. Using eigenvalues of G or eigenvalues of the complement of G, we in this note present sufficient conditions for the Hamiltonicity of G.