Marcela Lascsáková

On d-antimagic labelings of plane graphs

The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d -antimagic if for every positive integer s , the s -sided face weights form an arithmetic progression with a difference d . Such a labeling is called super if the smallest possible labels appear on the vertices. In the paper we examine the existence of such labelings for several families of plane graphs.

Wheels are cycle-antimagic

Abstract A simple graph G admits an H-covering if every edge in E ( G ) belongs to a subgraph of G isomorphic to H. An (a, d)-H-antimagic total labeling of a graph G admitting an H-covering is a bijective function from the vertex set V ( G ) and the edge set E ( G ) of the graph G onto the set of integers { 1 , 2 , … , | V ( G ) | + | E ( G ) | } such that for all subgraphs H ′ isomorphic to H, the sum of labels of all the edges and vertices belonging to H ′ constitute the arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super cycle-antimagic total labelings of wheel.

Total Edge Irregularity Strength of Toroidal Fullerene

A toroidal fullerene (toroidal polyhex) is a cubic bipartite graph embedded on the torus such that each face is a hexagon. An edge irregular total k-labeling of a graph G is such a labeling of the vertices and edges with labels 1, 2, … , k that the weights of any two different edges are distinct, where the weight of an edge is the sum of the label of the edge itself and the labels of its two endvertices. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength, tes(G). In this paper we determine the exact value of the total edge irregularity strength of toroidal polyhexes.

On H-irregularity strength of graphs

Abstract New graph characteristic, the total H-irregularity strength of a graph, is introduced. Estimations on this parameter are obtained and for some families of graphs the precise values of this parameter are proved.

Improving Accuracy of the Numerical Model Forecasting Commodity Prices

In mathematical models, for forecasting prices on commodity exchanges different mathematical methods are used. In the paper the numerical model based on the exponential approximation of commodity stock exchanges was derived. The price prognoses of aluminium on the London Metal Exchange were determined as numerical solution of the Cauchy initial problem for the 1st order ordinary differential equation. To make the numerical model more accurate the idea of the modification of the initial condition value by the stock exchange was realized. The derived numerical model was observed to determine the influence of the decreased size of the limiting value error causing the modification of the initial condition value by the chosen stock exchange on the accuracy of the obtained prognoses. The advantage of the chosen sizes of the limiting value error 7 % and 8 % within different movements of aluminium prices was studied.