A weighted directed graph G IS a triple (V, A . g) where (V. A) IS a directed graph and g is a n arbitrary real-valued function defined on the arc set A. Let G be a strongly-connected, simple weighted directed graph. We say tha t G is max-balanced if fo r every nontrivial ~ ubset of the vertices W, the maxImum weight over arcs leaving W equals the maximum weIght over arcs entering W. We show th...

In the Mixed Chinese Postman Problem (MCPP), given an edge-weighted mixed graph G (G may have both edges and arcs), our aim is to find a minimum weight closed walk traversing each edge and arc at least once. The MCPP parameterized by the number of edges was known to be fixed-parameter tractable using a simple argument. Solving an open question of van Bevern et al., we prove that the MCPP parame...

In this paper we study polynomials (Pn) which are hermitian orthogonal on two arcs of the unit circle with respect to weight functions which have square root singularities at the end points of the arcs, an arbitrary nonvanishing trigonometric polynomial A in the denominator and possible point measures at the zeros of A. First we give an explicit representation of the orthogonal polynomials Pn i...

A method is presented to interpolate real affine plane curves with second degree NURBS (Non Uniform Rational Bezier Splines). The curve into object is initially partitioned into an arbitrary number of arcs. Then each arc is approximated with a conic section passing thru its extremes, thru a third intermediate point and being tangent to the arc at the extremes. Each arc is then parameterized by ...

The notion of strong arcs in a fuzzy graph was introduced byBhutani and Rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. In Mordeson and Yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.In this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

The arc costs are assumed to be online parameters of the network and decisions should be made while the costs of arcs are not known. The policies determine the permitted nodes and arcs to traverse and they are generally defined according to the departure nodes of the current policy nodes. In on-line created tours arc costs are not available for decision makers. The on-line traversed nodes are f...

We study the problem of maintaining the distances and the shortest paths from a source node in a directed graph with arbitrary arc weights, when weight updates of arcs are performed. We propose algorithms that work for any digraph and have optimal space requirements and query time. If a negative{length cycle is introduced during weight-decrease operations it is detected by the algorithms. The p...

Linear sets on the projective line have attracted a lot of attention because their link with blocking sets, KM-arcs and rank-metric codes. In this paper, we study linear having two points complementary weight, that is, for which sum weights equals rank set. As special case, those exactly weight greater than one, by showing new examples studying equivalence issue. Also, determine some linearized...