Question

Frequencies for mobile radio (or cellular) telephones are assigned by zones. Each zone is assigned a set of frequencies to be used by vehicles in that zone. The same frequency cannot be used in different zones when interference can occur between telephones in these zones. Explain how a \(k - tuple\) coloring can be used to assign \(k\) frequencies to each mobile radio zone in a region.

Short answer

\(k - tuple\) coloring can be used to avoid interference of \(k\) frequencies to each mobile radio zone in a region.

Step-by-step solution

Given information

Given is \(k - tuple\).

Definition and formula to be used

A\(k - tuple\)coloring of a graph\(G\)is an assignment of a set of\(k\)different colors to each of the vertices of\(G\)such that no two adjacent vertices are assigned a common color.

Solution

Let the frequency be colors and zone be vertices.

Then, join two vertices with an edge of the zones. These vertices represent interference with one another.

Therefore, \(k - tuple\) coloring can be used to avoid interference of \(k\) frequencies to each mobile radio zone in a region.