Journal of Combinatorial Optimization

, Volume 14, Issue 2–3, pp 191–195 | Cite as

Near automorphisms of trees with small total relative displacements

  • Chia-Fen Chang
  • Hung-Lin Fu


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.


Near automorphism Tree Total relative displacement 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Chiao Tung UniversityHsin ChuTaiwan

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