   Constant 2-labelling of weighted cycles; Vandomme, Elise  Conference (2012, November) We introduce the concept of constant 2-labelling of a weighted graph and show how it can be used to obtain periodic sphere packing. Roughly speaking, a constant 2-labelling of a weighted graph is a 2 ... [more ▼] We introduce the concept of constant 2-labelling of a weighted graph and show how it can be used to obtain periodic sphere packing. Roughly speaking, a constant 2-labelling of a weighted graph is a 2-coloring (black and white) of its vertex set which preserves the sum of the weight of black vertices under some automorphisms. In this manuscript, we study this problem on weighted complete graphs and on weighted cycles. Our results on cycles allow us to determine (r,a,b)-codes in Z^2 whenever |a-b|>4 and r>1. [less ▲] Detailed reference viewed: 9 (1 ULg)Constant 2-labelling of a graph; Vandomme, Elise Conference (2012, September) We introduce the concept of constant 2-labelling of a weighted graph and show how it can be used to obtain periodic sphere packing. Roughly speaking, a constant 2-labelling of a weighted graph is a 2 ... [more ▼] We introduce the concept of constant 2-labelling of a weighted graph and show how it can be used to obtain periodic sphere packing. Roughly speaking, a constant 2-labelling of a weighted graph is a 2-coloring (black and white) of its vertex set which preserves the sum of the weight of black vertices under some automorphisms. In this manuscript, we study this problem on weighted complete graphs and on weighted cycles. Our results on cycles allow us to determine (r,a,b)-codes in Z^2 whenever |a-b|>4 and r>1. [less ▲] Detailed reference viewed: 2 (1 ULg)Coloring of the infinite gridVandomme, Elise ; Poster (2012, May 23) We present a method that links (r,a,b)-codes in the infinite grid and particular colorings of weighted cycles, called constant 2-labellings. Detailed reference viewed: 15 (2 ULg) |
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