Abstract
For a permutation f of the vertex set V(G) of a connected graph G, let δ f (x,y)=|d(x,y)−d(f(x),f(y))|. Define the displacement δ f (G) of G with respect to f to be the sum of δ f (x,y) over all unordered pairs {x,y} of distinct vertices of G. Let π(G) denote the smallest positive value of δ f (G) among the n! permutations f of V(G). In this note, we determine all trees T with π(T)=2 or 4.
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Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday.
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Chang, CF., Fu, HL. Near automorphisms of trees with small total relative displacements. J Comb Optim 14, 191–195 (2007). https://doi.org/10.1007/s10878-007-9062-8
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DOI: https://doi.org/10.1007/s10878-007-9062-8