Distance spectral radius and Hamiltonicity of a graph

In recent years, the eigenvalues of distance matrix a graph have attracted lot attention mathematicians, since there is close connection between its spectrum and structural properties graph. Thus, quite recently an interesting result was obtained, relating Hamiltonicity to spectral radius graph, on basis which more general conjecture about formulated. We confirm this put forward for k -connected when Î{2;3}, also establish similar sufficient conditions traceability Î{1; 2}.