Let k≥2 be an integer. A tree T is called a k-tree if dT​(v)≤k
for each v∈V(T), that is, the maximum degree of a k-tree is at most k.
Let λ1​(D(G)) denote the distance spectral radius in G, where D(G)
denotes the distance matrix of G. In this paper, we verify a upper bound for
λ1​(D(G)) in a connected graph G to guarantee the existence of a
spanning k-tree in G.Comment: 11 page