Some sufficient conditions on k-connected graphs

A connected graph G is said to be k-connected if it has more than k vertices and remains connected whenever fewer than k vertices are removed. Feng et al. (2017) presented sufficient conditions based on spectral radius for a graph to be k-connected, k-edge-connected, k-Hamiltonian, k-edge-Hamiltonian, β-deficient and k-path-coverable. In this paper, we present some further sufficient conditions for a graph to be k-connected in terms of signless Laplacian spectral radius, distance spectral radius, distance signless Laplacian spectral radius of G and Wiener index, Harary index of its complement.