On a relation between labeled graphs and permutations

AbstractIt has been shown that a connection can be made between labeled trees and representations of cyclic permutations by associating each edge (Xi,Xj) with a transposition tij. The same association can be applied to labeled graphs. It is shown that each element of the alternating group of permutations on m elements is representable by a product of transpositions associated with the edges of a complete graph of m vertices so long as the number of edges is even