Browsing by Author "Chang, Chia-Fen"

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Near automorphisms of cycles
(2008-04-06)
Chang, Chia-Fen
;
Chen, Bor-Liang
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
Let f be a permutation of V (G). Define delta(f)(x, y) = vertical bar d(G)(x, y) -d(G) (f (x), f (y))vertical bar and delta(f)(G) = Sigma delta(f)(x, y) over all the unordered pairs {x, y} of of distinct vertices of G. Let pi(G) denote the smallest positive value of delta(f)(G) among all the permutations f of V (G). The permutation f with delta(f) (G) = pi(G) is called a near automorphism of G. In this paper, we study the near automorphisms of cycles C and we prove that pi(C-n) = 4[n/2] - 4, moreover, we obtain the set of near automorphisms of C-n. (C) 2007 Elsevier B.V. All rights reserved.
Near automorphisms of trees with small total relative displacements
(2007-10-01)
Chang, Chia-Fen
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
For a permutation f of the vertex set V(G) of a connected graph G, let delta(f) (x,y)=vertical bar d(x,y) - d(f(x),f(y))vertical bar. Define the displacement delta(f) (G) of G with respect to f to be the sum of delta(f) (x,y) over all unordered pairs {x,y} of distinct vertices of G. Let pi(G) denote the smallest positive value of delta(f) (G) among the n! permutations f of V(G). In this note, we determine all trees T with pi(T) = 2 or 4.