let $g$ be a simple graph of order $n$ and size $m$.the edge covering of $g$ is a set of edges such that every vertex of $g$ is incident to at least one edge of the set. the edge cover polynomial of $g$ is the polynomial$e(g,x)=sum_{i=rho(g)}^{m} e(g,i) x^{i}$,where $e(g,i)$ is the number of edge coverings of $g$ of size $i$, and$rho(g)$ is the edge covering number of $g$. in this paper we stud...

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...

let $g$ be a connected graph of order $3$ or more and $c:e(g)rightarrowmathbb{z}_k$‎ ‎($kge 2$) a $k$-edge coloring of $g$ where adjacent edges may be colored the same‎. ‎the color sum $s(v)$ of a vertex $v$ of $g$ is the sum in $mathbb{z}_k$ of the colors of the edges incident with $v.$ the $k$-edge coloring $c$ is a modular $k$-edge coloring of $g$ if $s(u)ne s(v)$ in $mathbb{z}_k$ for all pa...

for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

let g=(v,e) be a simple graph. an edge labeling f:e to {0,1} induces a vertex labeling f^+:v to z_2 defined by $f^+(v)equiv sumlimits_{uvin e} f(uv)pmod{2}$ for each $v in v$, where z_2={0,1} is the additive group of order 2. for $iin{0,1}$, let e_f(i)=|f^{-1}(i)| and v_f(i)=|(f^+)^{-1}(i)|. a labeling f is called edge-friendly if $|e_f(1)-e_f(0)|le 1$. i_f(g)=v_f(1)-v_f(0) is called the edge-f...

We report the growth by ion exchange synthesis of ZnS nanoparticles in MCM-41 matrices using Zn (CH3COO)2 and Na2S starting sources. The final product (ZnS/MCM-41) was characterized by X-ray diffraction (XRD) pattern, transmission electron microscopy (TEM), scanning electron microscopy (SEM), infrared spectrometry (IR) and UV-vis spectroscopy. Its crystalline st...