Radio Labelings of Lexicographic Product of Some Graphs

Labeling of graphs has defined many variations in the literature, e.g., graceful, harmonious, and radio labeling. Secrecy of data in data sciences and in information technology is very necessary as well as the accuracy of data transmission and different channel assignments is maintained. It enhances the graph terminologies for the computer programs. In this paper, we will discuss multidistance radio labeling used for channel assignment problems over wireless communication. A radio labeling is a one-to-one mapping ℘ : V G ⟶ ℤ + satisfying the condition | ℘ μ − ℘ μ ′ | ≥ diam G + 1 − d μ , μ ′ : μ , μ ′ ∈ V G for any pair of vertices μ , μ ′ in G . The span of labeling ℘ is the largest number that ℘ assigns to a vertex of a graph. Radio number of G , denoted by r n G , is the minimum span taken over all radio labelings of G . In this article, we will find relations for radio number and radio mean number of a lexicographic product for certain families of graphs.

A semi-automated module for the separation and purification of 99mTc from simulated molybdenum target

A semi-automated purification module for the cyclic separation of 99mTc was designed for production of [99mTc]TcO4– from γ irradiated 100Mo target. The separation process was carried out by using a 3-column purification system and the final product, [99mTc]TcO4–, was obtained in a total volume of 7 mL. To confirm proper separation achieved for 99mTc, a radio-labeling procedure using DTPA chelator was performed. The radiochemical purity was higher than 95%, which meets the strict radiopharmaceutical requirements. The yielded 99mTc can be separated with high efficiency from Mo in a quick and repeated way. Loss of 99mTc radioactivity during such a three-column separation process was not larger than 10%.

On L h , k -Labeling Index of Inverse Graphs Associated with Finite Cyclic Groups

An L h , k -labeling of a graph G = V , E is a function f : V ⟶ 0 , ∞ such that the positive difference between labels of the neighbouring vertices is at least h and the positive difference between the vertices separated by a distance 2 is at least k . The difference between the highest and lowest assigned values is the index of an L h , k -labeling. The minimum number for which the graph admits an L h , k -labeling is called the required possible index of L h , k -labeling of G , and it is denoted by λ k h G . In this paper, we obtain an upper bound for the index of the L h , k -labeling for an inverse graph associated with a finite cyclic group, and we also establish the fact that the upper bound is sharp. Finally, we investigate a relation between L h , k -labeling with radio labeling of an inverse graph associated with a finite cyclic group.

The Radial Radio Number and the Clique Number of a Graph

Let G(V(G),E(G)) be a graph. A radial radio labeling, f, of a connected graph G is an assignment of positive integers to the vertices satisfying the following condition: d(u, v) | f (u)  f (v) | 1  r(G) , for any two distinct vertices u, v V(G) , where d(u,v) and r(G) denote the distance between the vertices u and v and the radius of the graph G, respectively. The span of a radial radio labeling f is the largest integer in the range of f and is denoted by span(f). The radial radio number of G, r(G) , is the minimum span taken over all radial radio labelingsof G. In this paper, we construct a graph a graph for which the difference between the radial radio number and the clique number is the given non negative integer.