This paper aims to develop a fast, parallelizable algorithm for an arbitrary decomposable semidefinite program (SDP). To formulate a decomposable SDP, we consider a multi-agent canonical form represented by a graph, where each agent (node) is in charge of computing its corresponding positive semidefinite matrix subject to local equality and inequality constraints as well as coupling and overlap...

Let $P(G,lambda)$ be the chromatic polynomial of a graph $G$. A graph $G$ ischromatically unique if for any graph $H$, $P(H, lambda) = P(G,lambda)$ implies $H$ is isomorphic to $G$. In this paper, we determine the chromaticity of all Tur'{a}n graphs with at most three edges deleted. As a by product, we found many families of chromatically unique graphs and chromatic equivalence classes of graph...

The Naive Mix is a new supervised learning algorithm based on sequential model selection. The usual objective of model selection is to nd a single proba-bilistic model that adequately characterizes, i.e. ts, the data in a training sample. The Naive Mix combines models discarded during the selection process with the best{{tting model to form an averaged probabilistic model. This is shown to impr...

let g be a fixed element of a finite group g. we introduce the g-noncommuting graph of g whose vertex set is whole elements of the group g and two vertices x,y are adjacent whenever [x,y] g  and  [y,x] g. we denote this graph by . in this paper, we present some graph theoretical properties of g-noncommuting graph. specially, we investigate about its planarity and regularity, its clique number a...

In this work we deal with the problem of learning a maximum weighted (k + 1)order decomposable graph coarser than a given maximal k-order decomposable graph. An Integer Linear Programming formulation for the problem has been recently proposed and used in order to solve instances of the problem with a moderate number of vertices [8]. However, as the problem is known to be NP-hard, it is of pract...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

We study two decomposition problems in combinatorial geometry. The first part of the thesis deals with the decomposition of multiple coverings of the plane. We say that a planar set is cover-decomposable if there is a constant m such that any m-fold covering of the plane with its translates is decomposable into two disjoint coverings of the whole plane. Pach conjectured that every convex set is...

Let G and H be connected graphs. The tensor product G + H is a graph with vertex set V(G+H) = V (G) X V(H) and edge set E(G + H) ={(a , b)(x , y)| ax ∈ E(G) & by ∈ E(H)}. The graph H is called the strongly triangular if for every vertex u and v there exists a vertex w adjacent to both of them. In this article the tensor product of G + H under some distancebased topological indices are investiga...

Throughout this paper, every groups are finite. The prime graph of a group $G$ is denoted by $Gamma(G)$. Also $G$ is called recognizable by prime graph if for every finite group $H$ with $Gamma(H) = Gamma(G)$, we conclude that $Gcong H$. Until now, it is proved that if $k$ is an odd number and $p$ is an odd prime number, then $PGL(2,p^k)$ is recognizable by prime graph. So if $k$ is even, the r...

A polynomial over a ring is called decomposable if it composition of two nonlinear polynomials. In this paper, we obtain sharp lower and upper bounds for the number polynomials with integer coefficients fixed degree bounded height. Moreover, asymptotic formulas monic even degree. For example, sextic which are height at most H to $$(16\zeta (3)-5/4)H^3$$ as $$H \rightarrow \infty $$ .