A graph G admits an H-covering if every edge of belongs to a subgraph isomorphic given H. is said be H-magic there exists bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that wf(H′)=∑v∈V(H′)f(v)+∑e∈E(H′)f(e) constant, for H′ In particular, H-supermagic f(V(G))={1,2,…,|V(G)|}. When H complete K2, H-(super)magic labeling edge-(super)magic labeling. Suppose F-covering and two graphs F We define (...

Abstract Cancer prevention and treatment are currently the focus of most research. Dose verification is an important step for reducing improper dose deposition during radiotherapy. To mend traditional gel dosimeters 3D verification, a novel rare-earth nanoparticle-based composite was prepared, which has good radioluminescence property reusability. It promising phantom material new dosimeter. TE...

introduction the purpose of the current study was to determine optical sensitivity of n-isopropyl acrylamide nipam and polyacrylamide gelatin and tetrakis hydroxymethyl phosphoniun chloride (pagat) polymer gels for different wavelength of visible light spectrum applied in optical computed tomography method. materials and methods nipam and pagat polymer gels with conventional formulations used f...

A (p, q)-graph G = (V, E) is said to be magic if there exists a bijection f : V ∪ E → {1, 2, 3, . . . , p + q} such that for all edges uv of G, f(u) + f(v) + f(uv) is a constant. The minimum of all constants say, m(G), where the minimum is taken over all such bijections of a magic graph G, is called the magic strength of G. In this paper we define the maximum of all constants say, M(G), analogo...

A graph G is called super edge-magic if there exists a bijective function f : V (G) ∪ E (G) → {1, 2, . . . , |V (G)|+ |E (G)|} such that f (V (G)) = {1, 2, . . . , |V (G)|} and f (u) + f (v) + f (uv) is a constant for each uv ∈ E (G). A graph G with isolated vertices is called pseudo super edge-magic if there exists a bijective function f : V (G) → {1, 2, . . . , |V (G)|} such that the set {f (...

An H-magic labeling in an H-decomposable graph G is a bijection f : V (G)∪E(G)→ {1, 2, . . . , p+ q} such that for every copy H in the decomposition, ∑ v∈V (H) f(v)+ ∑ e∈E(H) f(e) is constant. The function f is said to be H-E-super magic if f(E(G)) = {1, 2, . . . , q}. In this paper, we study some basic properties of m-factor-E-super magic labeling and we provide a necessary and sufficient cond...

background: the aim of this work was to establish how well gel dosimeters performed, as substitutes for brain tissue compared with standard phantom materials such as water, polymethyl-methacrylate (or pmma), a150 plastic and te- liquid phantom material for dosimetry of neutron beams in boron neutron capture therapy. materials and methods: thermal neutron fluence, photon dose and epithermal neut...