Radio Numbers of Generalized Petersen Graphs

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Jennifer Galovich, Mathematics


Assigning frequencies to radio transmitters to avoid interference presents an interesting problem in graph theory. When assigning frequencies to radio transmitters, transmitters that are geographically close must be assigned channels that have large differences in frequency, while transmitters that are further apart may be assigned channels with relatively close frequencies. The general situation can be modeled by representing the transmitters as vertices on a graph and then assigning positive integers to the vertices of a graph. As with transmitters and radio channels, vertices which are close together must be as assigned integers which are further apart, while vertices with greater distance between them can be assigned integers which are close together. The radio number of a graph is the minimum possible span of integers assigned to the vertices of the graph. I will present an upper bound for the radio number of a family of graphs called generalized Petersen graphs.

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