Labeling: Small 2/2009

Labeling proteins with small molecules by site-specific posttranslational modification.

We report here the development of a general strategy for site-specific labeling of proteins with small molecules by posttranslational modification enzyme, phosphopantetheinyl transferase Sfp. The target proteins are expressed as fusions to the peptide carrier protein (PCP) excised from nonribosomal peptide synthetase, and Sfp catalyzes the covalent modification of a specific serine residue on P...

Compact Ancestry Labeling Schemes for Trees of Small Depth

An ancestry labeling scheme labels the nodes of any tree in such a way that ancestry queries between any two nodes in a tree can be answered just by looking at their corresponding labels. The common measure to evaluate the quality of an ancestry labeling scheme is by its label size, that is the maximal number of bits stored in a label, taken over all n-node trees. The design of ancestry labelin...

k-equitable mean labeling

Remainder Cordial Labeling of Graphs

In this paper we introduce remainder cordial labeling of graphs. Let $G$ be a $(p,q)$ graph. Let $f:V(G)rightarrow {1,2,...,p}$ be a $1-1$ map. For each edge $uv$ assign the label $r$ where $r$ is the remainder when $f(u)$ is divided by $f(v)$ or $f(v)$ is divided by $f(u)$ according as $f(u)geq f(v)$ or $f(v)geq f(u)$. The function$f$ is called a remainder cordial labeling of $G$ if $left| e_{...

Labeling Subgraph Embeddings and Cordiality of Graphs

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...