The k-uniform s-hypertree G = （V, E） is an s-hypergraph, where 1 ≤ s ≤ k - 1, and there exists a host tree T with vertex set V such that each edge of G induces a connected subtree of T. In this paper, some propert...The k-uniform s-hypertree G = （V, E） is an s-hypergraph, where 1 ≤ s ≤ k - 1, and there exists a host tree T with vertex set V such that each edge of G induces a connected subtree of T. In this paper, some properties of uniform s-hypertrees are establised, as well as the upper and lower bounds on the largest H-eigenvalue of the adjacency tensor of k-uniform s-hypertrees in terms of the maximal degree A. Moreover, we also show that the gap between the maximum and the minimum values of the largest H-eigenvalue of k-uniform s-hypertrees is just （△S/k）.展开更多
Let S(m,d,k)be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k)be the k-uniform supertree obtained from a loose path u_(1),e_(1),u_(2),e_(2),...,u_(d),e_(d),u_(d+1),with length d by attaching ...Let S(m,d,k)be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k)be the k-uniform supertree obtained from a loose path u_(1),e_(1),u_(2),e_(2),...,u_(d),e_(d),u_(d+1),with length d by attaching m-d edges at vertex u_[d/2]+1.In this paper,we mainly determine S1(m,d,k)with the largest signless Laplacian spectral radius in S(m,d,k)for 3≤d≤m-1.We also determine the supertree with the second largest signless Laplacian spectral radius in S(m,3,k).Furthermore,we determine the unique/c-uniform supertree with the largest signless Laplacian spectral radius among all fc-uniform supertrees with n vertices and pendent edges(vertices).展开更多
Given a hypergraph H(V,E),a set of vertices S⊆V is a vertex cover if every edge has at least one vertex in S.The vertex cover number is the minimum cardinality of a vertex cover,denoted byτ(H).In this paper,we prove ...Given a hypergraph H(V,E),a set of vertices S⊆V is a vertex cover if every edge has at least one vertex in S.The vertex cover number is the minimum cardinality of a vertex cover,denoted byτ(H).In this paper,we prove that for every 3-uniform connected hypergraph H(V,E),τ(H)≤2m3+1/3 holds on where m is the number of edges.Furthermore,the equality holds on if and only if H(V,E)is a hypertree with perfect matching.展开更多
The explicit formula for (k+l)-uniform linear acyclic hypergraphs and the counting series for unlabeled (k +1)-uniform linear acyclic hypergraphs are obtained.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11471077）.
文摘The k-uniform s-hypertree G = （V, E） is an s-hypergraph, where 1 ≤ s ≤ k - 1, and there exists a host tree T with vertex set V such that each edge of G induces a connected subtree of T. In this paper, some properties of uniform s-hypertrees are establised, as well as the upper and lower bounds on the largest H-eigenvalue of the adjacency tensor of k-uniform s-hypertrees in terms of the maximal degree A. Moreover, we also show that the gap between the maximum and the minimum values of the largest H-eigenvalue of k-uniform s-hypertrees is just （△S/k）.
基金supported in part by the National Natural Science Foundation of China(Grant No.11871398)the Natural Science Foundation of Shaanxi Province(Nos.2020JQ-107,2020JQ-696)the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(Nos.ZZ2018171,CX2020190).
文摘Let S(m,d,k)be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k)be the k-uniform supertree obtained from a loose path u_(1),e_(1),u_(2),e_(2),...,u_(d),e_(d),u_(d+1),with length d by attaching m-d edges at vertex u_[d/2]+1.In this paper,we mainly determine S1(m,d,k)with the largest signless Laplacian spectral radius in S(m,d,k)for 3≤d≤m-1.We also determine the supertree with the second largest signless Laplacian spectral radius in S(m,3,k).Furthermore,we determine the unique/c-uniform supertree with the largest signless Laplacian spectral radius among all fc-uniform supertrees with n vertices and pendent edges(vertices).
基金This paper was supported by the National Natural Science Foundation of China (No. 11901605).
文摘Given a hypergraph H(V,E),a set of vertices S⊆V is a vertex cover if every edge has at least one vertex in S.The vertex cover number is the minimum cardinality of a vertex cover,denoted byτ(H).In this paper,we prove that for every 3-uniform connected hypergraph H(V,E),τ(H)≤2m3+1/3 holds on where m is the number of edges.Furthermore,the equality holds on if and only if H(V,E)is a hypertree with perfect matching.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19771040)and the Natural Science Foundation of Guangdong Province.
文摘The explicit formula for (k+l)-uniform linear acyclic hypergraphs and the counting series for unlabeled (k +1)-uniform linear acyclic hypergraphs are obtained.
