The minimum span of L(2,1)-labelings of certain generalized Petersen graphs

The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography

“…7 is an upper bound also for generalized Petersen graphs of order greater than 6. In [3,4] the authors prove that this conjecture is true for orders 7 and 8, and give exact λ 2,1 -numbers for all generalized Petersen graphs of orders 5, 7 and 8, thereby closing all cases with orders up to 8. Finally, in [5] the exact λ 2,1 -numbers for all generalized Petersen graphs of orders 9, 10, 11 and 12 are given, thereby closing all open cases up to order N = 12 and lowering the upper bound on λ 2,1 down to 6 for all but three graphs of these orders.…”

“…In [4,5] some subclasses of generalized Petersen graphs, particularly symmetric, are considered. The authors provide the exact λ 2,1 -numbers of such graphs, for any order.…”

Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs

“…In the recently published literature, various properties of GP (n, k) have been investigated: minimum span of L(2, 1)-labeling [1], minimum vertex cover [4], metric dimension [2,27], strong metric dimension [18], decycling number [13], component connectivity [10], acyclic 3-coloring [34], crossing numbers [25], independence number [11], and others. Some recent works dealing with variants of the domination numbers in the generalized Petersen graphs are: domination number [3,12,26], domatic number, total domatic number, and k-ply domatic number [33], efficient domination number [17], power domination number [32], 2-rainbow domination [5,31], and others.…”

\((d,1)\)-Total Labelling of Generalized Petersen Graphs \(P(n,k)\)

“…A number of articles has been devoted to the study of the labeling and coloring of P(n, k), in particular, to the study of L(2,1)-labeling and total coloring [16][17][18][19][20][21]. However, the (d, 1)-total labeling of generalized Petersen graphs still remains open.…”