A square difference 3-equitable labeling of a graph G with vertex set V is a bijection f from V to {1, 2,.... | V | } jg such that if each edge uv is assigned the label -1 if |[f (u)]2 [f (v)]2 | = -1(mod 4), the label 0 if |[f (u)]2 [f (v)]2 | = 0(mod 4) and the label 1 if |[f (u)]2 [f (v)]| = 1(mod 4), then the number of edges labeled with i and the number of edges labelled with j differ by a...

A 3-equitable prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, ..., |V |} such that if an edge uv is assigned the label 1 if gcd(f(u), f(v)) = 1 and gcd(f(u) + f(v), f(u)−f(v)) = 1, the label 2 if gcd(f(u), f(v)) = 1 and gcd(f(u) + f(v), f(u)− f(v)) = 2 and 0 otherwise, then the number of edges labeled with i and the number of edges labeled with j differ b...

There is a rich literature on conditions guaranteeing that certain sums of residue classes cover certain other residue classes modulo some integer N . Often it is of particular importance for applications to know that the class 0 mod N can be represented as a sum of the studied residue classes, and the zero class is often the most difficult case. A well-known result along these lines is the fam...

A square difference 3-equitable labeling of a graph G with vertex set V is a bijection f from V to {1, 2,.... | V | } jg such that if each edge uv is assigned the label -1 if |[f (u)]2 [f (v)]2 | = -1(mod 4), the label 0 if |[f (u)]2 [f (v)]2 | = 0(mod 4) and the label 1 if |[f (u)]2 [f (v)]| = 1(mod 4), then the number of edges labeled with i and the number of edges labelled with j differ by a...

A graph G is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest integer k for which such a coloring exists is known as the equitable chromatic number of G and it is denoted by χ=(G). In this paper the problem of determinig the value of equitable chromatic number for multic...

McNamara and Pylyavskyy conjectured precisely which connected skew shapes are maximal in the Schur-positivity order, which says that B ≤s A if sA − sB is Schurpositive. Towards this, McNamara and van Willigenburg proved that it suffices to study equitable ribbons, namely ribbons whose row lengths are all of length a or (a+ 1) for a ≥ 2. In this paper we confirm the conjecture of McNamara and Py...

transfusion-dependent patients such as those suffering from β-thalassaemia develop a fatal secondary haemosiderosis and consequently a selective iron chelator must be used to relieve such iron overload. 3- hydroxypyridin-4-ones are selective for iron(iii) under most biological conditions, but unlike desferrioxamine, are efficiently absorbed when administered orally. in this study, the synthesis...

iron overload is a serious clinical condition which can be largely prevented by the use of iron-specific chelating agents. in this study, the synthesis and determination of partition coefficients (kpart) of a range of n-alkyl hydroxypyridinones, as orally active iron chelators, are described. synthesis of n-aryl hydroxypyridinones was achieved via a single step synthetic pathway. in this method...