The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
A signed graph is a graph whose edges are labeled by signs. If has vertices, its spectral radius is the number , where are the eigenvalues of the signed adjacency matrix . Here we determine the signed graphs achieving the minimal or the maximal spectral radius in the classes and of unbalanced unicyclic graphs and unbalanced bicyclic graphs, respectively.
A graph is nonsingular if its adjacency matrix is nonsingular. The inverse of a nonsingular graph is a graph whose adjacency matrix is similar to via a particular type of similarity. Let denote the class of connected bipartite graphs with unique perfect matchings. Tifenbach and Kirkland (2009) characterized the unicyclic graphs in which possess unicyclic inverses. We present a characterization of unicyclic graphs in which possess bicyclic inverses.
One of the best known results in spectral graph theory is the following lower bound on the chromatic number due to Alan Hoffman, where μ1 and μn are respectively the maximum and minimum eigenvalues of the adjacency matrix: χ ≥ 1+μ1/−μn. We recently generalised this bound to include all eigenvalues of the adjacency matrix. In this paper, we further generalize these results to include all eigenvalues of the adjacency, Laplacian and signless Laplacian matrices. The various known bounds are also unified...
We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.
Currently displaying 1 –
7 of
7