Channel assignment and graph labeling
Handbook of wireless networks and mobile computing
On generalized Petersen graphs labeled with a condition at distance two
Discrete Mathematics
IWDC '02 Proceedings of the 4th International Workshop on Distributed Computing, Mobile and Wireless Computing
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Frequency Channel Assignment on Planar Networks
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Distance-two labelings of graphs
European Journal of Combinatorics
Labeling trees with a condition at distance two
Discrete Mathematics
Discrete Applied Mathematics
L(h,1)-labeling subclasses of planar graphs
Journal of Parallel and Distributed Computing
L(2, 1)-labeling of direct product of paths and cycles
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
A note on collections of graphs with non-surjective lambda labelings
Discrete Applied Mathematics
Optimal L(d,1)-labelings of certain direct products of cycles and Cartesian products of cycles
Discrete Applied Mathematics
The L(2, 1)-labelling of trees
Discrete Applied Mathematics
L(2, 1)-labelings of Cartesian products of two cycles
Discrete Applied Mathematics
Acyclic colorings of products of trees
Information Processing Letters
The 2-dipath chromatic number of Halin graphs
Information Processing Letters
A bound on the chromatic number of the square of a planar graph
Journal of Combinatorial Theory Series B
Distance-two labelings of digraphs
Discrete Applied Mathematics
The minimum span of L(2,1)-labelings of certain generalized Petersen graphs
Discrete Applied Mathematics
(2,1)-Total labelling of outerplanar graphs
Discrete Applied Mathematics
New bounds for the L(h, k) number of regular grids
International Journal of Mobile Network Design and Innovation
Optimal frequency assignments of cycles and powers of cycles
International Journal of Mobile Network Design and Innovation
Note: Improved upper bounds on the L(2,1) -labeling of the skew and converse skew product graphs
Theoretical Computer Science
Labelling planar graphs without 4-cycles with a condition on distance two
Discrete Applied Mathematics
On L(d,1)-labeling of Cartesian product of a cycle and a path
Discrete Applied Mathematics
A distance-labelling problem for hypercubes
Discrete Applied Mathematics
(2,1)-Total labelling of trees with sparse vertices of maximum degree
Information Processing Letters
A general approach to L(h,k)-label interconnection networks
Journal of Computer Science and Technology
(2,1)-Total number of trees with maximum degree three
Information Processing Letters
An O(n1.75) algorithm for L(2,1)-labeling of trees
Theoretical Computer Science
Notes: A note on collections of graphs with non-surjective lambda labelings
Discrete Applied Mathematics
L(2,1)-labeling of direct product of paths and cycles
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Optimal L(d,1)-labelings of certain direct products of cycles and Cartesian products of cycles
Discrete Applied Mathematics
Note: The L(2,1)-labelling of trees
Discrete Applied Mathematics
L(2,1)-labelings of Cartesian products of two cycles
Discrete Applied Mathematics
L(j,k)-labelling and maximum ordering-degrees for trees
Discrete Applied Mathematics
The (2,1)-total labeling number of outerplanar graphs is at most Δ + 2
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
A tight upper bound on the (2,1)-total labeling number of outerplanar graphs
Journal of Discrete Algorithms
Labeling Planar Graphs without 4,5-Cycles with a Condition on Distance Two
SIAM Journal on Discrete Mathematics
On the L(2,1)-labelings of amalgamations of graphs
Discrete Applied Mathematics
Path covering number and L(2,1)-labeling number 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
List backbone colouring of graphs
Discrete Applied Mathematics
| Hi-index | 0.01 |
An $L(2, l)$-labeling of graph $G$ is an integer labeling of $V(G)$ such that adjacent vertices have labels that differ by at least 2 and such that vertices distance 2 apart have labels that differ by at least 1. The $\lambda$-number of $G, \lambda(G)$, is the minimum range over all $L(2, 1)$-labelings. We examine the properties of $\lambda$-labelings of the $n$-cube $Q_n$. Griggs and Yeh have determined $\lambda(Q_n)$ for $n \leq 5$ and have established $n + 3 \leq \lambda(Q_n) \leq 2n + 1$ for $n \geq 6$. We modify a technique used in coding theory to improve the upper bound. We also examine the $\lambda$-labelings of related graphs, such as the subdivision of the $n$-cube and the Cartesian products of paths.