Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$.  For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...

a graceful labeling of a graph g of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of g, such that when each edge of g has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. if a graceful labeling f of a bipartite graph g assigns the smaller labels to one of the two stable sets of g, then f...

Edge-coloring total k-labeling of a connected graph G is an assignment f of non negative integers to the vertices and edges of G such that two adjacent edges e = uv and e = uv of G have different weights. The weight of an edge uv is defined by: w(e = uv) = f(u) + f(v) + f(e). In this paper, we study the chromatic number of the edge coloring by total labeling of 4-regular circulant graphs Cn(1, k).

A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...

labeling theory is one of the most famous theories in criminology domain. the pivots of this theory consist of the role of power owners in definition of crime and determination of offender, effects of labeling and solutions for prevention of entering label. with study the pivots of labeling theory in islamic sources, we observe that however there is no similarity between religious bases and bas...

lactobacilli, like the other gut commensal bacteria, are well known for their use in poultry nutrition and for their probiotic properties. however, little is known about their interaction with the gastro-intestinal tract when administered in vivo. to specifically monitor the passage of lactobacilli after administered in hatchery, lactobacillus plantarum was transformed with the recombinant vect...

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introduction: the field of stem cell biology and regenerative medicine is rapidly moving toward translation to clinical practice. stem cell therapy seems to be a new treatment option for some diseases. so, tracking the distribution of stem cells is crucial to their therapeutic use. based on this fact we labeled human mesenchymal stem cells (mscs) with 111in- oxine for the first time in our coun...

let $g=(v, e)$ be a graph. by emph{directional labeling (ord-labeling)} of an edge $x=uv$ of $g$ by an ordered $n$-tuple$(a_1,a_2,...,a_n)$, we mean a labeling of the edge $x$ such thatwe consider the label on $uv$ as $(a_1,a_2,...,a_n)$ in thedirection from $u$ to $v$, and the label on $x$ as$(a_{n},a_{n-1},...,a_1)$ in the direction from $v$ to $u$. inthis paper, we study graphs, called emph{...