, the copy of H(d ) is labeled with 1. Moreover, for
,
, D k is obtained from one copy of H(d) for every d ? {? ? k, ? ? k + 2, p.2
, = 1 for every edge e in E(D k ) \ {rc}, and any (k + 1)-labeling with mS(D k , ) = ? is such that (rc) ? {k, k + 1} and (e) the copies of H(d) (d ? {? ? k, ? ? k + 2, Moreover, the unique k-labeling with mS(D k , ) = ? is such that (rc) = k and (e)
, assuming the input of G is labeled 1, also its two outputs are labeled 1. A similar case analysis yields an analogous conclusion when (u 1 u 2 ) = 2, see Figure 5 (b). Let us point out that
and let G be the graph obtained by identifying o 1 (G 1 ) and i(G 2 ). Then, in every 2-labeling of G, all of i ,
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