A power digraph, denoted by $G(n,k)$, is a directed graph with $Z_{n}={0,1,..., n-1}$ as the set of vertices and $L={(x,y):x^{k}equiv y~(bmod , n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper, the structure of $G(2q+1,k)$, where $q$ is a Sophie Germain prime is investigated. The primality tests for the integers of the form $n=2q+1$ are established in terms of th...

the evaluation of the edge effects of forest roads on ecosystem is very useful to understand changes from forest road. with this regard, in this research the effect of main forest road construction on regeneration and biodiversity of established trees in edge of forest road was investigated at 35 m distance into forest area. an existing 10 years old road segment, with same physiographic propert...

one of the locations of renal artery atherosclerosis is at the orifice of the renal artery, therefore thestructure of this orifice was assessed in 6 normal, adult male dogs by light microscopy (lm) andtransmission electron microscopy (tem). for the lm study, processed tissues were embedded in paraffinand sectioned serially into 6-μm thickness. sections were stained with orcein. for the tem stud...

In this paper, we obtain some upper and lower bounds for the general extended energy of a graph. As an application, we obtain few bounds for the (edge) Zagreb energy of a graph. Also, we deduce a relation between Zagreb energy and edge-Zagreb energy of a graph $G$ with minimum degree $delta ge2$. A lower and upper bound for the spectral radius of the edge-Zagreb matrix is obtained. Finally, we ...

Graph theory plays an important role for modelling and designing chemical structures complex networks. Chemical graph is commonly used to analyse comprehend networks, as well their features. In theory, a structure can be represented by vertices edges where denote atoms molecular bonds. The concept of resolvability parameters G= (V, E) relatively new advanced field in which the complete built so...

Oxide nanoparticles can exhibit unique physical and chemical properties due to their limited size and a high density of corner or edge surface sites. In this study, MgO nanoparticle was synthesized using Mg(CH3COO)2 and hexamethylenetetramine as starting materials. The structure and optical properties of these particles are investigated by using X-ray diffraction (XRD), sc...

the topological indices, defined as the sum of contributions of all pairs of vertices (among which are the wiener, harary, hyper–wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.