The Inductive Graph Dimension from the Minimum Edge Clique Cover

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