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Achromatic index of $$K_{12}$$. (English) Zbl 0933.05048
The achromatic index of a graph $$G$$ is the maximum integer $$k$$ such that there exists a proper colouring of the edges (i.e. in which no two adjacent edges have the same colour) in which each pair of colours appear on some pair of adjacent edges. The achromatic index of the complete graph $$K_n$$ with $$n$$ vertices is denoted by $$A(n)$$. It is proved that $$A(12)=32$$.

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
achromatic index; edge colouring; complete graph