| Abstract: | Let  be a permutation of the vertex set V(G) of a connected graph G. Define the total relative displacement of in G by be where
dG(x, y)
is the length of the shortest path between x and y in G. Let  *
(G) be the maximum value of 
(G) among all permutations of V(G). The permutation which realizes *
(G) is called a chaotic mapping of G. In this paper, we study the chaotic mappings of complete multipartite graphs. The problem is reduced to a quadratic integer programming problem. We characterize its optimal solution and present an algorithm running in
time, where n is the total number of vertices in a complete multipartite graph. |
