Near automorphisms of trees with small total relative displacements |
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Authors: | Chia-Fen Chang Hung-Lin Fu |
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Institution: | (1) Department of Applied Mathematics, National Chiao Tung University, Hsin Chu, 30050, Taiwan |
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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.
Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday. |
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Keywords: | Near automorphism Tree Total relative displacement |
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