On prime labellings
The paper is devoted to the study of prime graphs, that is finite graphs that admit a prime labelling. A prime labelling of a graph \(G=(V,E)\) is a bijection \(f: V\to \{1,2,\dots,| V|\}\) such that if \(e= \{u,v\}\in E\) then \(\text{GCD}(f(u),f(v))= 1\). Some results concerning bipartite graphs are obtained; all trees of order up to 15 are proved to be prime graphs. Such a result is a partial answer to the conjecture that all trees are prime graphs.
scientific article; zbMATH DE number 562629