Name
Abstract | ||
|---|---|---|
(d,1)-total labelling of a graph G assigns integers to the vertices and edges of G such that adjacent vertices receive distinct labels, adjacent edges receive distinct labels, and a vertex and its incident edges receive labels that differ in absolute value by at least d. The span of a (d,1)-total labelling is the maximum difference between two labels. The (d,1)-total number, denoted @l"d^T(G), is defined to be the least span among all (d,1)-total labellings of G. We prove new upper bounds for @l"d^T(G), compute some @l"d^T(K"m","n) for complete bipartite graphs K"m","n, and completely determine all @l"d^T(K"m","n) for d=1,2,3. We also propose a conjecture on an upper bound for @l"d^T(G) in terms of the chromatic number and the chromatic index of G. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.disc.2008.10.008 | Discrete Mathematics |
Keywords | Field | DocType |
l( 2,channel assignment,-total labelling,chromatic number,chromatic index,1 ) -labelling,1 ) -total labelling,( d,l ( 2,1)-labelling,upper bound,complete bipartite graph,indexation | Integer,Complete graph,Discrete mathematics,Edge coloring,Combinatorics,Vertex (geometry),Upper and lower bounds,Absolute value,Bipartite graph,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
309 | 12 | Discrete Mathematics |
Citations | PageRank | References |
11 | 0.66 | 9 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ko-wei Lih | 1 | 529 | 58.80 |
| Daphne Der-Fen Liu | 2 | 232 | 26.32 |
| Weifan Wang | 3 | 868 | 89.92 |