Is this definition of a complete bipartite graph correct? The book I am using defined a complete graph $K_{m,n} = \overline{K}_m + \overline{K}_n$. Is this correct? I am confused since the complement of a complete graph is an empty graph. How is the addition of two empty graph a complete bipartite graph if we follow the definition?

Some authors use $G+H$ to indicate the graph join, which is a copy of $G$ and a copy of $H$ together with every edge between $G$ and $H$. This is IMO unfortunate, since $+$ makes more sense as disjoint union. (Authors who use $+$ for join probably use either $G\cup H$ or $G\sqcup H$ for the disjoint union.)
