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Flows on the join of two graphs

Robert Lukoťka; Edita Rollová — 2013

Mathematica Bohemica

The join of two graphs $G$ and $H$ is a graph formed from disjoint copies of $G$ and $H$ by connecting each vertex of $G$ to each vertex of $H$ . We determine the flow number of the resulting graph. More precisely, we prove that the join of two graphs admits a nowhere-zero $3$ -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...

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