Let G be a non-abelian group. The non-commuting graph AG of G is defined as the graph whose vertex set is the non-central elements of G and two vertices are joint if and only if they do not commute. In a finite simple graph Γ the maximum size of a complete subgraph of Γ is called the clique number of Γ and it is denoted by ω(Γ). In this paper we characterize all non-solvable groups G with ω(AG)...

In this paper, we present a new method for the study of a discrete random variable whose probability distribution has a finite support. The approach is based on the introduction of a transform of the probability density function, named γ-transform, which better suits the finite nature of the random variable than the traditional probability generating function. In particular, in addition to the ...

Let G be a simple graph with e perfectly reliable edges and n nodes which fail independently and with the same probability ρ. The residual connectedness reliability R(G, ) ρ of G is the probability that the graph induced by the surviving nodes is connected. If Γ(n, e) is the collection of all n node e edge simple graphs, then G n e ∈Γ( , ) is uniformly most reliable if R G R G ( , ) ( , ) ρ ρ ≥...

In this paper, we study the asymmetric traveling salesman problem (ATSP) with strengthened triangle inequality, i.e. for some γ ∈ [ 1 2 , 1) the edge weights satisfy w(u, v) ≤ γ(w(u, x) + w(x, v)) for all distinct vertices u, v, x. We present two approximation algorithms for this problem. The first one is very simple and has approximation ratio 1 2(1−γ) , which is better than all previous resul...

The commuting graph of a group G, denoted by Γ(G), is the simple undirected graph whose vertices are the non-central elements of G and two distinct vertices are adjacent if and only if they commute. Let Zm be the commutative ring of equivalence classes of integers modulo m. In this paper we investigate the connectivity and diameters of the commuting graphs of GL(n,Zm) to contribute to the conje...

If p2 : Γ → U is proper, Γ∗ = pr1∗ ◦ pr∗ 2 : H c (U,Q ) → H c (U,Q ) is defined. Write Tr(Γ∗ : H∗ c (UF̄ ,Q )) = ∑2d q=0(−1)Tr(Γ : H c (UF̄ ,Q )). Assume X: smooth U ⊂ X: the complement of a divisor D = D1 ∪ · · · ∪ Dm with simple normal crossings. Define p : (X ×X)′ → X ×X: the blow-up at D1 ×D1, . . . , Dm ×Dm ∆X = X → (X ×X)′: the log diagonal. Theorem 1.2 Let Γ̄′ be the closure of Γ in (X ×X)′...

We consider the problem of scheduling a set of independent jobs on a single machine where a solution is evaluated with respect to two min-sum objective functions: the sum of completion times and the sum of weighted completion times. In particular, we are interested in (α,β)-approximate schedules, i.e., schedules which are simultaneously at most α times from the optimum for the first objective, ...

this work presents a numerical analysis of entropy generation in γ-shaped enclosure that was submitted to the natural convection process using a simple thermal lattice boltzmann method (tlbm) with the boussinesq approximation.  a 2d thermal lattice boltzmann method with 9 velocities, d2q9, is used to solve the thermal flow problem. the simulations are performed at a constant prandtl number (pr ...

Background and objectivesAmino acid neurotransmitters are closely correlated to the neurological function of brain, imbalance amino can lead a variety diseases. Therefore, development simple method detect five (aspartate, glutamate, glycine, taurine, γ-aminobutyric) in brain is urgently needed.

A complement to a database view Γ is a second view Γ ′ which provides the information necessary to reconstruct the entire state of the main schema. View complementation is central in situations in which a view is to be updated, since the complement Γ ′ embodies the information not contained in Γ . In general, Γ may have many complements. In this work, an approach to identifying and constructing...