University of Isfahan Transactions on Combinatorics 2251-8657 5 3 2016 09 01 Extreme edge-friendly indices of complete bipartite graphs 11 21 12473 10.22108/toc.2016.12473 EN Wai Chee Shiu Hong Kong Baptist University Journal Article 2015 09 30 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 $f^+(v)\equiv \sum\limits_{uv\in E} f(uv)\pmod{2}$ for each $v \in V$‎, ‎where $Z_2=\{0,1\}$ is the additive group of order 2‎. ‎For $i\in\{0,1\}$‎, ‎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-friendly index of $G$ under an edge-friendly labeling $f$‎. ‎Extreme values of edge-friendly index of complete bipartite graphs will be determined‎. https://toc.ui.ac.ir/article_12473_5cd474dbde30ab0cf85638c76d56808a.pdf