-Labeling of the Strong Product of Paths and Cycles

Algorithm 1

Procedure  CREATE GRAPH(𝑖,𝑘,𝑁);

begin

𝑉³_𝑖,𝑘:= set of all 𝑘-𝐿(2,1)-labelings of 𝐶_𝑛⊠𝑃₃;

for all  𝑣=𝑣₁𝑣₂𝑣₃∈𝑉³_𝑖,𝑘 do  Insert 𝑣₁𝑣₂ in 𝑉²_𝑖,𝑘;

Sort vertices 𝑢₁𝑢₂ of 𝑉²_𝑖,𝑘 with respect to 𝑢₁, vertices with the same value of 𝑢₁ sort with respect to 𝑢₂;

for all  𝑣=𝑣₁𝑣₂𝑣₃∈𝑉³_𝑖,𝑘 do

 Find 𝑢=𝑢₁𝑢₂ in 𝑉²_𝑖,𝑘 such that 𝑢₁=𝑣₁ and 𝑢₂=𝑣₂;

 Find 𝑤=𝑤₁𝑤₂ in 𝑉²_𝑖,𝑘 such that 𝑤₁=𝑣₂ and 𝑤₂=𝑣₃;

 Insert 𝑤 in 𝑁_𝑢;

end.