Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
On generalized Petersen graphs labeled with a condition at distance two
Discrete Mathematics
L(h,1)-labeling subclasses of planar graphs
Journal of Parallel and Distributed Computing
Circular Distance Two Labeling and the $\lambda$-Number for Outerplanar Graphs
SIAM Journal on Discrete Mathematics
A bound on the chromatic number of the square of a planar graph
Journal of Combinatorial Theory Series B
Labeling planar graphs with a condition at distance two
European Journal of Combinatorics
$L(2,1)$-Labeling of Hamiltonian graphs with Maximum Degree 3
SIAM Journal on Discrete Mathematics
Graph Theory
The Computer Journal
Griggs and Yeh's Conjecture and $L(p,1)$-labelings
SIAM Journal on Discrete Mathematics
| Hi-index | 0.04 |
An L(2,1)-labeling of a graph G is an assignment of a non-negative integer to each vertex of G such that adjacent vertices receive integers that differ by at least two and vertices at distance two receive distinct integers. The span of such a labeling is the difference between the largest and smallest integers used. The @l-number of G, denoted by @l(G), is the minimum span over all L(2,1)-labelings of G. Bodlaender et al. conjectured that if G is an outerplanar graph of maximum degree @D, then @l(G)@?@D+2. Calamoneri and Petreschi proved that this conjecture is true when @D=8 but false when @D=3. Meanwhile, they proved that @l(G)@?@D+5 for any outerplanar graph G with @D=3 and asked whether or not this bound is sharp. In this paper we answer this question by proving that @l(G)@?@D+3 for every outerplanar graph with maximum degree @D=3. We also show that this bound @D+3 can be achieved by infinitely many outerplanar graphs with @D=3.