Name
Abstract | ||
|---|---|---|
Let C"m be the cycle of length m. We denote the Cartesian product of n copies of C"m by G(n,m):=C"m@?C"m@?...@?C"m. The k-distance chromatic number @g"k(G) of a graph G is @g(G^k) where G^k is the kth power of the graph G=(V,E) in which two distinct vertices are adjacent in G^k if and only if their distance in G is at most k. The k-distance chromatic number of G(n,m) is related to optimal codes over the ring of integers modulo m with minimum Lee distance k+1. In this paper, we consider @g"2(G(n,m)) for n=3 and m=3. In particular, we compute exact values of @g"2(G(3,m)) for 3@?m@?8 and m=4k, and upper bounds for m=3k or m=5k, for any positive integer k. We also show that the maximal size of a code in Z"6^3 with minimum Lee distance 3 is 26. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.dam.2011.07.022 | Discrete Applied Mathematics |
Keywords | Field | DocType |
cartesian product,distinct vertex,2-distance coloring,k-distance chromatic number,minimum lee distance k,n copy,graph g,minimum lee distance,optimal lee code,positive integer k,length m,integers modulo m | Integer,Discrete mathematics,Combinatorics,Lee distance,Chromatic scale,Vertex (geometry),Modulo,Cartesian product,Ring of integers,Code (cryptography),Mathematics | Journal |
Volume | Issue | ISSN |
159 | 18 | 0166-218X |
Citations | PageRank | References |
2 | 0.44 | 16 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jon-Lark Kim | 1 | 312 | 34.62 |
| Seog-Jin Kim | 2 | 151 | 17.63 |