We introduce joins of signed graphs and explore the chromatic number of the all-positive and all-negative joins. We prove an analogue to the theorem that the chromatic number of the join of two graphs equals the sum of their chromatic numbers. Given two signed graphs, the chromatic number of the all-positive and all-negative join is usually less than the sum of their chromatic numbers, by an amount that depends on the new concept of deficiency of a signed-graph coloration.

中文翻译：

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有符号图的连接的色数

我们介绍了有符号图的连接并探索了全正和全负连接的色数。我们证明了定理的一个类比，即两个图的连接的色数等于它们的色数之和。给定两个有符号图，全正和全负连接的色数通常小于它们的色数之和，其数量取决于有符号图着色缺陷的新概念。