Eigenvalues Variation. I.

Eigenvalues and forbidden subgraphs I

Suppose a graph G have n vertices, m edges, and t triangles. Letting λn (G) be the largest eigenvalue of the Laplacian of G and μn (G) be the smallest eigenvalue of its adjacency matrix, we prove that λn (G) ≥ 2m2 − 3nt m (n2 − 2m) , μn (G) ≤ 3n3t− 4m3 nm (n2 − 2m) , with equality if and only if G is a regular complete multipartite graph. Moreover, if G is Kr+1-free, then λn (G) ≥ 2mn (r − 1) (...

Bounds on graph eigenvalues I

We improve some recent results on graph eigenvalues. In particular, we prove that if G is a graph of order n 2; maximum degree ; and girth at least 5; then

Laplacian eigenvalues and optimality: I. Block designs

Variation of the Discrete Eigenvalues of Normal Operators

The Hooman{Wielandt inequality which gives a bound for the distance between the spectra of two normal matrices, is generalized to normal operators A; B on a separable Hilbert space, such that A ? B is Hilbert{Schmidt.

Eigenvalues-based LSB steganalysis

So far, various components of image characteristics have been used for steganalysis, including the histogram characteristic function, adjacent colors distribution, and sample pair analysis. However, some certain steganography methods have been proposed that can thwart some analysis approaches through managing the embedding patterns. In this regard, the present paper is intended to introduce a n...