In this paper we prove that the inductively defined graph dimension has a simple additive property under the join operation. The dimension of the join of two simple graphs is one plus the sum of the dimensions of the component graphs: \(\mathrm {dim\,} (G_1+ G_2) = 1 +\mathrm {dim\,} G_1+ \mathrm {dim\,} G_2\). We use this formula to derive an expression for the inductive dimension of an arbitrary finite simple graph from its minimum edge clique cover. A corollary of the formula is that any arbitrary finite simple graph whose maximal cliques are all of order N has dimension \(N{-}1\). We finish by finding lower and upper bounds on the inductive dimension of a simple graph in terms of its clique number.

在本文中，我们证明了归纳定义的图维度在连接操作下具有简单的可加性。两个简单图的连接维数是 1 加上分量图的维数之和：\(\mathrm {dim\,} (G_1+ G_2) = 1 +\mathrm {dim\,} G_1+ \mathrm {dim \,} G_2\)。我们使用这个公式从任意有限简单图的最小边团覆盖推导出其归纳维数的表达式。该公式的一个推论是，任何最大团都是N阶的任意有限简单图具有维度\(N{-}1\)。我们通过根据其团数找到简单图的归纳维数的下限和上限来结束。