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 generalized Petersen graphs labeled with a condition at distance two
Discrete Mathematics
On Regular Graphs Optimally Labeled with a Condition at Distance Two
SIAM Journal on Discrete Mathematics
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
The minimum span of L(2,1)-labelings of certain generalized Petersen graphs
Discrete Applied Mathematics
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On L(2,1)-labeling of generalized Petersen graphs
Journal of Combinatorial Optimization
| Hi-index | 0.04 |
An L(2,1)-labeling of a graph G is an assignment f of nonnegative integers to the vertices of G such that if vertices x and y are adjacent, |f(x)-f(y)|=2, and if x and y are at distance two, |f(x)-f(y)|=1. The @l-number of G is the minimum span over all L(2,1)-labelings of G. A generalized Petersen graph (GPG) of order n consists of two disjoint copies of cycles on n vertices together with a perfect matching between the two vertex sets. By presenting and applying a novel algorithm for identifying GPG-specific isomorphisms, this paper provides exact values for the @l-numbers of all GPGs of orders 9, 10, 11, and 12. For all but three GPGs of these orders, the @l-numbers are 5 or 6, improving the recently obtained upper bound of 7 for GPGs of orders 9, 10, 11, and 12. We also provide the @l-numbers of several infinite subclasses of GPGs that have useful representations on Mobius strips.