vol22_pp151-160. 122KB Jun 04 2011 12:06:12 AM
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We give a necessary and sufficient condition for a graph to be bipartite in terms of an eigenvector corresponding to the largest eigenvalue of the adjacency matrix of the graph..
The purpose of the present letter is to elucidate this relation between tight mappings, the maximal multiplicity of the second eigenvalue of graph Laplacians and Courant’s nodal
Weighted graph, Generalized Bethe tree, Laplacian matrix, Adjacency matrix, Spectral radius, Algebraic connectivity.. AMS
Assume that the contrary holds, i.e., suppose that there is a graph G of type-III such that G has the greatest maximum eigenvalue in G( n, ∆).. We consider the next
Furthermore, we show that the largest maximum eigenvalue in such classes of trees is strictly monotone with respect to some partial ordering of degree sequences.. Thus, we extend
A real matrix with nonnegative entries and having a largest eigenvalue of multiplicity just one has a strictly positive left eigenvector (see the Appendix) if and only if there
The path, the complete graph, the cycle, the star and some quasi-star graphs, together with their complement graphs were shown to be determined by their Laplacian spectra [6, 9,
These results are used to characterize all extremal weighted trees with the largest p -Laplacian spectral radius among all weighted trees with a given degree sequence and a
