an existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius

Let n1, n2, . . . , nk be integers and v1, v2, . . . , vk be disjoint vertex sets with |vi| = ni foreach i = 1, 2, . . . , k. a k-partite k-uniform hypergraph on vertex classes v1, v2, . . . , vk is defined to bethe k-uniform hypergraph whose edge set consists of the k-element subsets s of v1 ∪ v2 ∪ · · · ∪ vk suchthat |s ∩ vi| = 1 for all i = 1, 2, . . . , k. we say that it is balanced if n1 = n2 = · · · = nk. in thispaper, we give a distance spectral radius condition to guarantee the existence of perfect matching ink-partite k-uniform hypergraphs, this result generalize the result of zhang and lin [perfect matchingand distance spectral radius in graphs and bipartite graphs, discrete appl. math., 304 (2021) 315-322].