Automorphisms of trivalent graphs

Let G"g","b be the set of all uni/trivalent graphs representing the combinatorial structures of pant decompositions of the oriented surface @S"g","b of genus g with b boundary components. We describe the set A"g","b of all automorphisms of graphs in G"g","b showing that, up to suitable moves changing the graph within G"g","b, any such automorphism can be reduced to elementary switches of adjacent edges.