T-coloring of graphs with application to frequency assignment in cellular mobile networks

Using the matrix semi-tensor product, this paper investigates the T-coloring problems of graphs with application to frequency assignment in cellular mobile networks, and presents a number of new results and algorithms. Firstly, the T-coloring problem is studied by using the matrix semi-tensor product, and two necessary and sufficient conditions are put forward for T-colorability, based on which a new algorithm is designed to find all the T-coloring schemes for any simple graph. Secondly, a kind of frequency assignment problem is discussed by using the obtained results, and a method to design a feasible assignment scheme is presented. Finally, the effectiveness of the results/algorithms presented in this paper is shown by two illustrative examples.