Name
Abstract | ||
|---|---|---|
For a positive integer n is an element of N and a set D subset of N, the distance graph G(n)(D) has vertex set {0, 1, ... , n - 1} and two vertices i and j of G(n)(D) are adjacent exactly if vertical bar j - i vertical bar is an element of D. The condition gcd (D) = 1 is necessary for a distance graph G(n)(D) being connected. Let D = {d(1), d(2)} subset of N be such that d(1) > d(2) and gcd (d(1), d(2)) = 1. We prove the following results. If n is sufficiently large in terms of D, then G(n)(D) has a Hamiltonian path with endvertices 0 and n - 1. If d(1)d(2) is odd, n is even and sufficiently large in terms of D, then G(n)(D) has a Hamiltonian cycle. If d(1)d(2) is even and n is sufficiently large in terms of D, then G(n)(D) has a Hamiltonian cycle. |
Year | Venue | Keywords |
|---|---|---|
2014 | DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE | Distance graph,Toeplitz graph,circulant graph,Hamiltonian path,Hamiltonian cycle,traceability |
Field | DocType | Volume |
Integer,Discrete mathematics,Graph,Combinatorics,Circulant graph,Vertex (geometry),Hamiltonian (quantum mechanics),Hamiltonian path,Hamiltonian path problem,Mathematics | Journal | 16.0 |
Issue | ISSN | Citations |
1.0 | 1462-7264 | 0 |
PageRank | References | Authors |
0.34 | 21 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christian Löwenstein | 1 | 131 | 16.28 |
| Dieter Rautenbach | 2 | 946 | 138.87 |
| Roman Soták | 3 | 128 | 24.06 |