Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a0-1 labeling of $E(G)$ so that the absolute difference in the number of edgeslabeled 1 and 0 is no more than one. Call such a labeling $f$\emph{edge-friendly}. We say an edge-friendly labeling induces a \emph{partialvertex labeling} if vertices which are incident to more edges labeled 1 than 0,are labeled 1, and vertices which are incident to more edges labeled 0 than 1,are labeled 0. Vertices that are incident to an equal number of edges of bothlabels we call \emph{unlabeled}. Call a procedure on a labeled graph a\emph{label switching algorithm} if it consists of pairwise switches of labels.Given an edge-friendly labeling of $K_n$, we show a label switching algorithmproducing an edge-friendly relabeling of $K_n$ such that all the vertices arelabeled. We call such a labeling \textit{opinionated}.
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机译：设$ G $为顶点集为$ V（G）$且边集为$ E（G）$的图，而$ f $为$ E（G）$的a0-1标签，这样数的绝对差标记为1和0的边的总数不超过1。称此类标签为$ f $ \ emph {edge-friendly}。我们说，如果将入射到标记为1的边多于0的边的顶点标记为1，将入射到标记为0的边多于1的顶点的顶点标记为0，则边缘友好标记会引发\ emph {partialvertex labeling}。入射到两个标签的等边沿的数量相同的情况，我们称之为\ emph {unlabeled}。如果它由标签的成对切换组成，则在标签图上调用一个过程\\ mph {标签交换算法}。鉴于$ K_n $的边沿友好标记，我们展示了一种标签交换算法，该算法产生$ K_n $的边沿友好重新标记这样就标记了所有顶点。我们称这种标签为\ textit {opinionated}。
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