Flows on the join of two graphs
The join of two graphs and is a graph formed from disjoint copies of and by connecting each vertex of to each vertex of . We determine the flow number of the resulting graph. More precisely, we prove that the join of two graphs admits a nowhere-zero -flow except for a few classes of graphs: a single vertex joined with a graph containing an isolated vertex or an odd circuit tree component, a single edge joined with a graph containing only isolated edges, a single edge plus an isolated...