Search

Uniform hypergraphs have a natural one-to-one correspondence to tensors. In this paper, we investigate the Estrada index and subgraph centrality of an m -uniform hypergraph H via the adjacency tensor. We establish some bounds for the Estrada index and give expressions of the subgraph centrality in terms of graph parameters of the multi-digraphs associated with H. When H is 2-uniform, the above Estrada index and subgraph centrality are the Estrada index and subgraph centrality of a graph. [ABSTRACT FROM AUTHOR]

Let G be a simple graph with n vertices. Let A ~ α G = α D G + 1 − α A G , where 0 ≤ α ≤ 1 and A G and D G denote the adjacency matrix and degree matrix of G , respectively. E E α G = ∑ i = 1 n e λ i is called the α -Estrada index of G , where λ 1 , ⋯ , λ n denote the eigenvalues of A ~ α G . In this paper, the upper and lower bounds for E E α G are given. Moreover, some relations between the α -Estrada index and α -energy are established. [ABSTRACT FROM AUTHOR]

Let and be two order m dimension n tensors. The Hadamard product is an order m dimension n tensor with entries . For nonnegative tensors and , we obtain some bounds on spectral radius of in terms of spectral radius and entries of and . We give some inequalities for the minimum eigenvalue and determinant of the Hadamard product involving M-tensors and Z-tensors, and use them to derive some criteria of M-tensors. [ABSTRACT FROM AUTHOR]

For a tensor A = ( a i 1 ⋯ i m ) ∈ C n × ⋯ × n , the associated digraph of A has the vertex set V ( A ) = { 1 , … , n } , and the arc set of Γ A is E ( A ) = { ( i , j ) | a i i 2 ⋯ i m ≠ 0 , j ∈ { i 2 , … , i m } ≠ { i , … , i } } . In this paper, we give some characterizations of M -tensors and H -tensors by using the associated digraph of a tensor. [ABSTRACT FROM AUTHOR]

In this paper, we obtain formulas for resistance distances and Kirchhoff index of subdivision graphs. An application of resistance distances to the bipartiteness of graphs is given. We also give an interlacing inequality for eigenvalues of the resistance matrix and the Laplacian matrix. [ABSTRACT FROM AUTHOR]

Abstract: Let G be a mixed graph with a nonzero Laplacian eigenvalue μ of multiplicity k. A line star set for μ in G is a set Y of k edges of G such that μ is not a Laplacian eigenvalue of . It is shown that line star set exists for any nonzero Laplacian eigenvalue of any mixed graph. Some basic properties for line star sets are given. We also obtain some results on line star sets in undirected graphs. [Copyright &y& Elsevier]

By using digraphs of tensors, we give Brualdi-type eigenvalue inclusion sets of tensors. We also give some applications of our result to nonsingularity and positive definiteness of tensors. [ABSTRACT FROM AUTHOR]