In this paper, we use methods from spectral graph theory to obtain some results on the sum-product problem over finite valuation rings R of order qr which generalize recent results given by Hegyvári and Hennecart (2013). More precisely, we prove that, for related pairs of two-variable functions f(x, y) and g(x, y), if A and B are two sets in R∗ with |A| = |B| = qα, then max {|f(A,B)|, |g(A,B)|}...

We consider a fundamental algorithmic question in spectral graph theory: Compute a spectral sparsifier of a random-walk matrix-polynomial

Spectral graph theory has proven to be a useful tool in the analysis of high-dimensional data sets. Recall that, mathematically, a graph is a collection of objects (nodes) and connections between them (edges); a weighted graph additionally assigns numerical values (weights) to the edges. Graphs are represented by their adjacency whose elements are the weights between the nodes. Spectral graph t...

let $g = (v, e)$ be a simple graph. denote by $d(g)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $a(g)$ the adjacency matrix of $g$. the  signless laplacianmatrix of $g$ is $q(g) = d(g) + a(g)$ and the $k-$th signless laplacian spectral moment of  graph $g$ is defined as $t_k(g)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

The Laplacian-energy-like of a simple connected graph G is defined as LEL:=LEL(G)=∑_(i=1)^n√(μ_i ), Where μ_1 (G)≥μ_2 (G)≥⋯≥μ_n (G)=0 are the Laplacian eigenvalues of the graph G. Some upper and lower bounds for LEL are presented in this note. Moreover, throughout this work, some results related to lower bound of spectral radius of graph are obtained using the term of ΔG as the num...

My research interests lie in spectral and extremal graph theory, as well as in the analysis of complex networks. A primary goal is to deduce fundamental structural graph properties from the spectrum of the graph or a few easily-computable invariants. In order to gain control over these invariants, extremal graph theory aims to tightly bound them and characterize the graphs achieving these bound...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...