WebFeb 18, 2024 · This matrix can be interpreted as the opposite of the adjacency matrix, which is instead constructed from the distance matrix of a graph by keeping each row and each column only the distances... WebWe will bound and derive the eigenvalues of the Laplacian matrices of some fundamental graphs, including complete graphs, star graphs, ring graphs, path graphs, and products of these that yield grids and hypercubes. As all these graphs are connected, they all have …

Star (graph theory) - Wikipedia

WebSep 5, 2015 · The eigenvalues should be n − 1, with multiplicity 1, and − 1, with multiplicity n − 1. The best way to see this in this particular case is through explicitly giving the eigenvectors. First, the graph K n is ( n − 1) -regular; a k -regular graph always has k as an eigenvalue with eigenvector j (the all-ones vector). Webeigenvalues ±(n − k) in the Star graphs Sn and presented such formulas for 2 k 5. Moreover, a lower bound on multiplicity of eigenvalues of Sn for sufficiently large n was obtained. It was proved that for a fixed integer eigenvalue of the Star graph Sn, its multiplicity is at least 2 1 2 nlogn(1−o(1)) [4]. rotary palermo

eigenvalue of a graph - Mathematics Stack Exchange

WebA star graph consists of a single central vertex together with voutlying vertices each of which is connected only to the central vertex by a bond (figure 1). Hence there are … WebFeb 1, 2024 · The Star graph S n = Cay ( Sym Ω, S) is the Cayley graph over the symmetric group Sym Ω with the generating set S. It was shown in [4] that the spectrum … WebMay 16, 2024 · 1 Answer Sorted by: 0 If a d -regular graph G is such that the second-largest eigenvalue λ of A ( G) is significantly smaller than d i.e., d − λ = Ω ( 1) d, then the graph is a good expander --all sets S with no more than half the number of vertices in them have Ω ( S ) neighbours outside. stove top burner covers rectangular