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
On the size of graphs labeled with condition at distance two
Journal of Graph Theory
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
Graph labeling and radio channel assignment
Journal of Graph Theory
L(2, 1)-labelings of Cartesian products of two cycles
Discrete Applied Mathematics
Distance-two labelings of digraphs
Discrete Applied Mathematics
The minimum span of L(2,1)-labelings of certain generalized Petersen graphs
Discrete Applied Mathematics
Optimal frequency assignments of cycles and powers of cycles
International Journal of Mobile Network Design and Innovation
On L(d,1)-labeling of Cartesian product of a cycle and a path
Discrete Applied Mathematics
L(2,1)-labelings of Cartesian products of two cycles
Discrete Applied Mathematics
Exact λ-numbers of generalized Petersen graphs of certain higher-orders and on Möbius strips
Discrete Applied Mathematics
L(2,1) -labelling of generalized prisms
Discrete Applied Mathematics
Labeling outerplanar graphs with maximum degree three
Discrete Applied Mathematics
On L(2,1)-labeling of generalized Petersen graphs
Journal of Combinatorial Optimization
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An L(2, 1)-labeling of graph G is an integer labeling of the vertices in V(G) such that adjacent vertices receive labels which differ by at least two, and vertices which are distance two apart receive labels which differ by at least one. The λ-number of G is the minimum span taken over all L(2, 1)-labelings of G. In this paper, we consider the λ-numbers of generalized Petersen graphs. By introducing the notion of a matched sum of graphs, we show that the λ-number of every generalized Petersen graph is bounded from above by 9. We then show that this bound can be improved to 8 for all generalized Petersen graphs with vertex order 12, and, with the exception of the Petersen graph itself, improved to 7 otherwise.