let $g=(v,e)$ be a connected simple graph. a labeling $f:v to z_2$ induces two edge labelings $f^+, f^*: e to z_2$ defined by $f^+(xy) = f(x)+f(y)$ and $f^*(xy) = f(x)f(y)$ for each $xy in e$. for $i in z_2$, let $v_f(i) = |f^{-1}(i)|$, $e_{f^+}(i) = |(f^{+})^{-1}(i)|$ and $e_{f^*}(i) = |(f^*)^{-1}(i)|$. a labeling $f$ is called friendly if $|v_f(1)-v_f(0)| le 1$. for a friendly labeling $f$ of...

background and purpose : there has been no report in which preoperative evaluation of adc for prediction of post therapeutic outcome was presented. the aim of our study was to retrospectively evaluation the use of the apparent diffusion coefficient (adc) for the prediction of malignancy and the outcome of malignant astrocytic tumors. methods: we reviewed mri of 26 male and 14 female patients wi...

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...

let z2 = {0, 1} and g = (v ,e) be a graph. a labeling f : v → z2 induces an edge labeling f* : e →z2 defined by f*(uv) = f(u).f (v). for i ε z2 let vf (i) = v(i) = card{v ε v : f(v) = i} and ef (i) = e(i) = {e ε e : f*(e) = i}. a labeling f is said to be vertex-friendly if | v(0) − v(1) |≤ 1. the vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. in this paper ...

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...

‎‎let $g=(v,e)$ be a simple graph‎. ‎an edge labeling $f:eto {0,1}$ induces a vertex labeling $f^+:vtoz_2$ 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(...

Let Z2 = {0, 1} and G = (V ,E) be a graph. A labeling f : V → Z2 induces an edge labeling f* : E →Z2 defined by f*(uv) = f(u).f (v). For i ε Z2 let vf (i) = v(i) = card{v ε V : f(v) = i} and ef (i) = e(i) = {e ε E : f*(e) = i}. A labeling f is said to be Vertex-friendly if | v(0) − v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper ...

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When estimating the labeling index is of interest, the design of experiments raises a number of methodological questions: How many cells should be scored? How big a difference in labeling index is likely to be detectable? What is the potential effect of low growth fraction on detecting a treatment effect? What are appropriate ways of expressing treatment effects on labeling index? Data from two...