Distance spectral radius and Hamiltonicity of a graph

Abstract

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