A signed graph (G,Σ) is a G together with set Σ⊆E(G) of negative edges. circuit positive if the product signs its edges positive. balanced all circuits are The frustration index l(G,Σ) minimum cardinality E⊆E(G) such that (G−E,Σ−E) balanced, and k-critical l(G,Σ)=k l(G−e,Σ−e)<k, for every e∈E(G). We study decomposition subdivision critical graphs completely determine t-critical graphs, t≤2. Cri...

Natural protein molecules are exceptional polymers. Encoded in apparently random strings of amino-acids, these objects perform clear physical tasks that are rare to find by simple chance. Accurate folding, specific binding, powerful catalysis, are examples of basic chemical activities that the great majority of polypeptides do not display, and are thought to be the outcome of the natural histor...

Predicting when a person might be frustrated can provide an intelligent system with important information about when to initiate interaction. For example, an automated Learning Companion or Intelligent Tutoring System might use this information to intervene, providing support to the learner who is likely to otherwise quit, while leaving engaged learners free to discover things without interrupt...

CONTEXT Athletic training students (ATSs) are involved in various situations during the clinical experience that may cause them to express levels of frustration. Understanding levels of frustration in ATSs is important because frustration can affect student learning, and the clinical experience is critical to their development as professionals. OBJECTIVE To explore perceived levels of frustra...

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...