‎Let $G=(V,E)$ be a connected simple graph‎. ‎A labeling $f:V to Z_2$ induces an edge labeling‎ ‎$f^*:E to Z_2$ defined by $f^*(xy)=f(x)+f(y)$ for each $xy in E$‎. ‎For $i in Z_2$‎, ‎let‎ ‎$v_f(i)=|f^{-1}(i)|$ and ...