WebStar-like trees axe trees homeomorphic to stars. In this paper we identify those star-like trees for which the second largest eigenvalue is extremal — either minimal or maximal — when certain conditions are imposed. We also obtain partial results on the way in which the second largest eigenvalue of a simple class of star-like trees changes ... WebAn application to Paley graphs 44 8. Eigenvalues of graphs 46 Adjacency and laplacian eigenvalues 46 First properties 48 First examples 50 9. Eigenvalue computations 52 ...
1 Eigenvalues of graphs - Massachusetts Institute of …
Web(2) if the eigenvalue cursco with multiplicity mul( ) in ˆ^(f), then the multiplicity of in Ais P kdim(V)mul( ). This general result was used by G. Chapuy and V. eraFy to give the formula for multiplicities of eigenaluesv of the Star graph S … WebFeb 1, 2024 · Given an n-vertex graph G=(V,E), the Laplacian spectrum of G is the set of eigenvalues of the Laplacian matrix L=D-A, where D and A denote the diagonal matrix … how do you say fifth in spanish
THE MAIN EIGENVALUES OF A GRAPH: A SURVEY - JSTOR
Web1 Eigenvalues of graphs Looking at a graph, we see some basic parameters: the maximum degree, the minimum degree, its connectivity, maximum clique, maximum … WebApr 11, 2024 · Moreover, if G is connected, then equality holds if and only if G is either a star \(K_{1,n-1}\) or a complete graph \(K_n\). ... Mohar B (2009) On the sum of \(k\) largest eigenvalues of graphs and symmetric matrices. J Combin Theory Ser B 99:306–313. Article MathSciNet MATH Google Scholar Nikiforov V (2015) Extrema of graph … 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). how do you say ferrero rocher