T-colorings of graphs: recent results and open problems
Discrete Mathematics - Special issue: advances in graph labelling
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
Relating path coverings to vertex labellings with a condition at distance two
Discrete Mathematics
On the $\lambda$-Number of $Q_n$ and Related Graphs
SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
On L(d, 1)-labelings of graphs
Discrete Mathematics
Labeling Products of Complete Graphs with a Condition at Distance Two
SIAM Journal on Discrete Mathematics
Distance-two labelings of graphs
European Journal of Combinatorics
A Theorem about the Channel Assignment Problem
SIAM Journal on Discrete Mathematics
Note: L(2,1)-Labelings on the composition of n graphs
Theoretical Computer Science
New upper bounds on the L(2,1)-labeling of the skew and converse skew product graphs
Theoretical Computer Science
| Hi-index | 5.24 |
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 @l(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 @l(G)@?@D^2 for any simple graph with maximum degree @D=2. This paper considers the graph formed by the skew product and the converse skew product of two graphs with a new approach on the analysis of adjacency matrices of the graphs as in [W.C. Shiu, Z. Shao, K.K. Poon, D. Zhang, A new approach to the L(2,1)-labeling of some products of graphs, IEEE Trans. Circuits Syst. II: Express Briefs (to appear)] and improves the previous upper bounds significantly.