Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...

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...

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...

Snapping biceps femoris tendon (BFT) over the fibular head is an uncommon cause of lateral knee pain, with few case reports in the literature.1–12 Reported causes include anomalous tendon insertion, tears at the tendon insertion site, abnormality of the fibular head, and tendon subluxation despite normal anatomy. When nonoperative management fails, various surgical treatment techniques have bee...

OBJECTIVES To estimate oculometric parameters of Graves' ophthalmopathy in comparison to healthy eyes using digital photography and digital image analysis. INTRODUCTION Graves' ophthalmopathy is the main cause of eye proptosis. Because these protrusions cause clinically perceived distortions in orbital architecture, digital photographs can be used to detect and quantify these changes. METHO...

The purpose of this study was to investigate whether treatment with the Tip-Edge appliance resulted in more apical root resorption (ARR) of the central and lateral incisors during the torquing (third stage) than the non-torquing phases (first two stages) of orthodontic treatment. The three stages of this orthodontic technique make it possible to examine the amount of root shortening during torq...