the synthesis of [cu3o(oac)6(h2o)3]cl.ch3oh.6h2o is described. the x-ray crystallographic study of thecomplex revealed an isosceles triangle of copper atoms with a triply bridging oxo atom nearly in the plane of thetriangle. the coordination sphere around each metal center is close to distorted octahedral and the central{cu3(μ3-o)} core is planar. every two copper atoms were connected to each o...

a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...

A variation of the channel assignment problem is naturally modeled by L(2, 1)-labelings of graphs. An L(2, 1)-labeling of a graph G is an assignment of labels from {0, 1, . . . , λ} to the vertices of G such that vertices at distance two get different labels and adjacent vertices get labels that are at least two apart and the λ-number λ(G) of G is the minimum value λ such that G admits an L(2, ...

The quadratic assignment problem (QAP) is very challengeable and interesting problem that can model many real-life problems. In this paper, we will simply discuss the meaning of quadratic assignment problem, solving techniques and we will give a survey of some developments and researches.

It was recently demonstrated that a well-known eigenvalue bound for the Quadratic Assignment Problem (QAP) actually corresponds to a semideenite programming (SDP) relaxation. However, for this bound to be computationally useful the assignment constraints of the QAP must rst be eliminated, and the bound then applied to a lower-dimensional problem. The resulting \projected eigenvalue bound" is on...

We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semideenite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the well-known projected eigenvalue bound, and appears to be competitive with existing bounds in the tradeoo between bound quality and computational eeort.

This paper reports heuristic and exact solution advances for the Quadratic Assignment Problem (QAP). QAP instances most often discussed in the literature are relatively well solved by heuristic approaches. Indeed, solutions at a fraction of one percent from the best known solution values are rapidly found by most heuristic methods. Exact methods are not able to prove optimality for these instan...

Local search procedures are popular methods to solve combinatorial problems and neighborhood structures are the main part of those algorithms. This paper presents a new neighborhood for the Quadratic Assignment Problem. The proposed neighborhood is compared with the classical 2-exchange neighborhood.