An edge irregular total k-labeling of a graph G is a labeling of the vertices and edges with labels 1, 2, . . . , k such 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 end vertices. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregul...

A k-total-coloring of G is an assignment of k colors to the edges and vertices of G, so that adjacent and incident elements have different colors. The total chromatic number of G, denoted by χT (G), is the least k for which G has a k-total-coloring. It was proved by Rosenfeld that the total chromatic number of a cubic graph is either 4 or 5. Cubic graphs with χT = 4 are said to be Type 1, and c...

in wheat na+ exclusion and k+/na+ have shown to be associated with salinity tolerance, therefore in order to identify qtls with additive effect for na+ and k+ concentration traits in roots and shoots of wheat, 319  bread wheat recombinant inbred lines (ril f7), derived from a cross between roshan cultivar (salt tolerant) and falat cultivar (salt sensitive), along with their parents and 2 checks...

Given a poset P = (X,≺), a partition X1, . . . ,Xk of X is called an ordered partition of P if, whenever x ∈ Xi and y ∈ Xj with x ≺ y, then i ≤ j. In this paper, we show that for every poset P = (X,≺) and every integer k ≥ 2, there exists an ordered partition of P into k parts such that the total number of comparable pairs within the parts is at most (m− 1)/k, where m ≥ 1 is the total number of...

In this article, we study shape fitting problems, -coresets, and total sensitivity. We focus on the (j, k)-projective clustering problems, including k-median/k-means, k-line clustering, j-subspace approximation, and the integer (j, k)-projective clustering problem. We derive upper bounds of total sensitivities for these problems, and obtain -coresets using these upper bounds. Using a dimension-...

In this study some selected chemical properties such as total soluble solids, pH, total acidity, formalin index, reduced sugar content and ascorbic acid of major sour cherry cultivated grown in different provinces of Iran corresponding were investigated.  Minerals K+, Na+, Ca2+, Mg2+, Cu2+, Fe2+ and Zn2+ were determine...