Near automorphisms of trees with small total relative displacements

Chia-Fen Chang () and Hung-Lin Fu
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Chia-Fen Chang: National Chiao Tung University
Hung-Lin Fu: National Chiao Tung University

Journal of Combinatorial Optimization, 2007, vol. 14, issue 2, No 9, 195 pages

Abstract: 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.

Keywords: Near automorphism; Tree; Total relative displacement (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10878-007-9062-8

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