Distance spectral radius and edge-disjoint spanning trees

The spanning tree packing number of a graph G , denoted by τ ( G ) , is the maximum number of edge-disjoint spanning trees contained in G . In 2012, Cioabă and Wong initiated a study of τ ( G ) from spectral perspectives. Since this work, τ ( G ) has been well studied by using the second-largest eigenvalue of the adjacency matrix. In this paper, we provide the distance spectral radius conditions to guarantee that τ ( G ) ≥ k in a (bipartite) graph.