Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
Labeling trees with a condition at distance two
Discrete Mathematics
Real Number Graph Labellings with Distance Conditions
SIAM Journal on Discrete Mathematics
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
The Channel Assignment Problem with Variable Weights
SIAM Journal on Discrete Mathematics
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Real Number Channel Assignments for Lattices
SIAM Journal on Discrete Mathematics
Bounds for the Real Number Graph Labellings and Application to Labellings of the Triangular Lattice
SIAM Journal on Discrete Mathematics
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
On real number labelings and graph invertibility
Discrete Applied Mathematics
| Hi-index | 0.04 |
For integer r=2, the infinite r-path P"~(r) is the graph on vertices ...v"-"3,v"-"2,v"-"1,v"0,v"1,v"2,v"3... such that v"s is adjacent to v"t if and only if |s-t|@?r-1. The r-path on n vertices is the subgraph of P"~(r) induced by vertices v"0,v"1,v"2,...,v"n"-"1. For non-negative reals x"1 and x"2, a @l"x"""1","x"""2-labeling of a simple graph G is an assignment of non-negative reals to the vertices of G such that adjacent vertices receive reals that differ by at least x"1, vertices at distance two receive reals that differ by at least x"2, and the absolute difference between the largest and smallest assigned reals is minimized. With @l"x"""1","x"""2(G) denoting that minimum difference, we derive @l"x"""1","x"""2(P"n(r)) for r=3, 1@?n@?~, and x"1x"2@?[2,~]. For x"1x"2@?[1,2], we obtain upper bounds on @l"x"""1","x"""2(P"~(r)) and use them to give @l"x"""1","x"""2(P"~(r)) for r=5 and x"1x"2@?[1,2r-22r-3]@?[43,2]. We also determine @l"x"""1","x"""2(P"~(3)) and @l"x"""1","x"""2(P"~(4)) for all x"1x"2@?[1,2].