Web17 de jan. de 2024 · How to prove that the spectral radius of a linear operator is the infimum over all subordinate norms of the corresponding norm of the operator. So along those lines $$ \rho(AU) = \inf_{\left\lVert \cdot \right\rVert} \left\lVert AU \right\rVert $$ Just suppose for a second that the infimum is achieved and let $\left\lVert U \right\rVert_{M}$ … Web19 de jun. de 2024 · In this article, we introduce a Laplacian for the reciprocal distance matrix of a connected graph, called the reciprocal distance Laplacian. Let $$\\delta …
Spectral radius of a matrix multiplied by a contraction matrix
WebThe generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy … Web5 de dez. de 2024 · The weighted adjacency matrix A f ( G ) of a graph G is a square matrix, where the ( i , j ) -entry is equal to f ( d i , d j ) if the vertices v i and v j are adjacent and 0 otherwise. Li and Wang [22] tried to unify methods to study spectral radius of weighted adjacency matrices of graphs weighted by various topological indices. how many ncaa football teams
On the distance $α$-spectral radius of a connected graph
Web9 de dez. de 2024 · Abstract. The distance Laplacian matrix of a connected graph is defined as , where is the distance matrix of and is the diagonal matrix of vertex transmissions of . The largest eigenvalue of is called the distance Laplacian spectral radius of . In this paper, we determine the graphs with maximum and minimum distance … Web25 de jun. de 2024 · where x is a vector of size m. I have experiments for randomly initialized matrices that satisfy the above conditions. All of these matrices have spectral radii less than or equal to 1. For the case when the spectral radius is equal to 1, the process still converges in my experiment. (Note that the matrix ( A T E) k converges to a non-zero ... Web1 de mar. de 2024 · The adjacency matrix A = A ( G) of the graph G is defined so that its ( i, j )-entry is equal to 1 if vivj ∈ E ( G) and 0 otherwise. Let λ 1 ≥ λ 2 ≥ ⋯ ≥ λ n − 1 ≥ λ n … how many nclex questions in 2022