Name
Abstract | ||
|---|---|---|
An L(2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x)−f(y)|≥2 if d(x,y)=1 and |f(x)−f(y)|≥1 if d(x,y)=2, where d(x,y) denotes the distance between x and y in G. The L(2,1)-labeling number λ(G) of G is the smallest number k such that G has an L(2,1)-labeling with max{f(v):v∈V(G)}=k. Griggs and Yeh conjecture that λ(G)≤Δ2 for any simple graph with maximum degree Δ≥2. This paper considers the graph formed by the Cartesian sum of two graphs. As corollaries, the new graph satisfies the above conjecture (with minor exceptions). |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.aml.2007.08.010 | Applied Mathematics Letters |
Keywords | Field | DocType |
Channel assignment,L(2,1)-labeling,Graph Cartesian sum | Integer,Mathematical analysis,Degree (graph theory),Conjecture,Cartesian coordinate system,Discrete mathematics,Graph,Mathematical optimization,Combinatorics,Vertex (geometry),Bound graph,Mathematics,Graph labelling | Journal |
Volume | Issue | ISSN |
21 | 8 | 0893-9659 |
Citations | PageRank | References |
1 | 0.38 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhendong Shao | 1 | 67 | 8.60 |
| David Zhang | 2 | 5068 | 234.25 |