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
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
Smallest independent dominating sets in Kronecker products of cycles
Discrete Applied Mathematics
Labeling Products of Complete Graphs with a Condition at Distance Two
SIAM Journal on Discrete Mathematics
L(2,1)-labelings of Cartesian products of two cycles
Discrete Applied Mathematics
On the L(2,1)-labelings of amalgamations of graphs
Discrete Applied Mathematics
L(2,1)-labelings of the edge-path-replacement of a graph
Journal of Combinatorial Optimization
L(d,1)-labelings of the edge-path-replacement of a graph
Journal of Combinatorial Optimization
| Hi-index | 0.05 |
An L(d,1)-labeling of a graph G is an assignment of nonnegative integers to the vertices such that adjacent vertices receive labels that differ by at least d and those at a distance of two receive labels that differ by at least one, where d=1. Let @l"1^d(G) denote the least @l such that G admits an L(d,1)-labeling using labels from {0,1,...,@l}. We prove that (i) if d=1, k=2 and m"0,...,m"k"-"1 are each a multiple of 2^k+2d-1, then @l"1^d(C"m"""0x...xC"m"""k"""-"""1)==1, k=1 and m"0,...,m"k"-"1 are each a multiple of 2k+2d-1, then @l"1^d(C"m"""0@?...@?C"m"""k"""-"""1)=