Article ID Journal Published Year Pages File Type
4652812 Electronic Notes in Discrete Mathematics 2007 7 Pages PDF
Abstract

Given a finite abelian group G, consider the complete graph on the set of all elements of G. Find a Hamiltonian cycle in this graph and for each pair of consecutive vertices along the cycle compute their sum. What are the smallest and the largest possible number of distinct sums that can emerge in this way? What is the expected number of distinct sums if the cycle is chosen randomly? How the answers change if an orientation is given to the cycle and differences (instead of sums) are computed? We give complete solutions to some of these problems and establish reasonably sharp estimates for the rest.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics