The study of graph labellings has focused on finding classes of graphs which admit a particular type of labelling. Here we consider variations of the well-known edge-magic and vertex-magic total labellings for which all graphs admit such a labelling. In particular, we consider two types of injections of the vertices and edges of a graph with positive integers: (1) for every edge the sum of its ...

Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V (G) to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum (under the operation of A) of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V (G) to A such that the weights of ...

Given a simple graph G (V, E) and a positive number d, an Ld(2, 1)-labelling of G is a function f V(G) [0, oc) such that whenever x, y E V are adjacent, If(x)f(Y)l >2d, and whenever the distance between x and y is two, If(x) f(Y)l >d. The Ld(2, 1)-labelling number A(G, d) is the smallest number m such that G has an Ld(2, 1)-labelling f with max{f(v) v E V} m. It is shown that to determine A(G, ...

We introduce two notions, (i)oriented labelling and (ii) oriented labelling, to explore frequency assignment problem under halfduplex setting and compute bounds of oriented labelling of special classes of graphs : trees, bipartite graphs and planar graphs. We do study an oriented version of clique cover problem as well. The frequency assignment problem (FAP) arises in wireless communication sys...

An L(2, 1)-labelling of a graph G is an assignment of non-negative integers to the vertices of G such that vertices at distance at most two get different numbers and adjacent vertices get numbers which are at least two apart. The L(2, 1)-labelling number of G, denoted by λ(G), is the minimum range of labels over all such labellings. In this paper, we first discuss some necessary and sufficient ...

background: ubi 29-41 (a derivative of antimicrobial peptide ubiquicidin) labelled with 99mtc is reported to discriminate between bacterial infections and sterile inflammatory processes. in this study, three lyophilized kit were performed, one of them based on the direct labelling with only sncl2 as reducing agent , and other two based on 6- hydrazinopyridine-3-carboxylic acid (hynic) and trici...