Hamiltonicity of \(k\)-connected Graphs with Independent Claws

In this paper, we prove that if \(G\) is a \(k\)-connected (\(k \geq 2\)) graph of order \(n\) such that the sum of degrees of any \(k+1\) independent vertices is at least \(n+k\), and if the set of claw centers of \(G\) is independent, then \(G\) is hamiltonian.