Name
Abstract | ||
|---|---|---|
The frequency assignment problem (FAP) is the assignment of frequencies to television and radio transmitters subject to restrictions imposed by the distance between transmitters. One of the graph theoretical models of FAP which is well elaborated is the concept of distance constrained labeling of graphs. Let G = (V, E) be a graph. For two vertices u and v of G, we denote d(u, v) the distance between u and v. An L(2, 1)-labeling for G is a function f : V -> {0, 1, ...} such that vertical bar f(u) - f(v)vertical bar >= 1 if d(u, v) = 2 and vertical bar f(u) - f(v)vertical bar >= 2 if d(u, v) = 1. The span of f is the difference between the largest and the smallest number of f(V). The lambda-number for G, denoted by lambda(G), is the minimum span over all L(2, 1)-labelings of G. In this paper, we study the lambda-number of the Cartesian and strong product of two directed cycles. We show that for m, n >= 4 the lambda-number of (C-m) over right arrow square(C-n) over right arrow is between 4 and 5. We also establish the lambda-number of (C) over right arrow (m) boxed times (C) over right arrow (n) for m <= 10 and prove that the lambda-number of the strong product of cycles (C) over right arrow (m) boxed times (C) over right arrow (n) is between 6 and 8 for m, n >= 48. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.3934/mfc.2018003 | MATHEMATICAL FOUNDATIONS OF COMPUTING |
Keywords | DocType | Volume |
Frequency assignment, radio coloring, L(2, 1)-labeling, Cartesian product, strong product | Journal | 1 |
Issue | ISSN | Citations |
1 | 2008-3289 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zehui Shao | 1 | 119 | 30.98 |
| huiqin jiang | 2 | 3 | 3.83 |
| Aleksander Vesel | 3 | 0 | 0.34 |