The zero eigenvalue of the Laplacian tensor of a uniform hypergraph (Q6546562)

In this paper, the author studies the algebraic multiplicity of the zero Laplacian eigenvalues of a connected uniform hypergraph. We can see the definition of a multi-array \(\mathcal A\) of \(n^k\) entries in \(\mathbb{C}\) at the beginning of Section 2. The notion of eigenvalue and eigenvector of \(\mathcal A\) is given in definition 2.1.\N\NThe definition of \(k\)-uniform hypergraph \(H\) appears at the top of page 1098, as does the definition of the degree of a vertex of \(H\). In definition 2.5 we can see the notion of the adjacency tensor of \(H\) and the Laplacian tensor of \(H\).\N\NThe main result of this paper is Theorem 3.2. It is an important result in this matter.\N\NIn Section 4, the author studies the problem with hyperstars and hyperpaths (definitions at the beginning of Section 4). The main result of this section is Theorem 4.9.\N\NThe proofs of all results of this paper are easy to read. The author finishes the paper with an interesting conjecture. I think this is one of the first of many other works on this interesting subject.