Radio fuzzy graphs and assignment of frequency in radio stations

Based on the rules of the Federal Communications Commission (FCC) of the United States, there is a problem when FM radio stations are situated nearby and transmit on channels when they are satisfactorily far separated. The difficulty of taking an optimal assignment of channels for a particular set of radio stations according to some given limitations on the distances among the stations as well as other factors are referred to as the Channel Assignment Problem. That problem has been designed mathematically in different ways. In this problem, it is managed by the introduction of radio k-colourings of graphs for assignment of frequency in radio stations. Depending on radio distances, radio fuzzy graphs have been defined. Complete radio fuzzy graphs, cyclic radio fuzzy graphs, and star radio fuzzy graphs are introduced, and several properties have been proved. Based on these theories, a survey on Kolkata (India) radio stations has been verified.

[1]  Frank Harary,et al.  Radio labelings of graphs , 2001 .

[2]  Esmail Keshavarz.  Vertex-coloring of fuzzy graphs: A new approach , 2016, J. Intell. Fuzzy Syst..

[3]  Madhumangal Pal,et al.  Fuzzy colouring of fuzzy graphs , 2016 .

[4]  Daniel Král,et al.  A Theorem about the Channel Assignment Problem , 2003, SIAM J. Discret. Math..

[5]  Gary Chartrand,et al.  A graph labeling problem suggested by FM channel restrictions , 2005 .

[6]  Pratima Panigrahi,et al.  A lower bound for radio k-chromatic number , 2015, Discret. Appl. Math..

[7]  Pawan Kumar,et al.  ON RADIO NUMBER OF POWER OF CYCLES , 2011 .

[8]  Jerrold R. Griggs,et al.  Labelling Graphs with a Condition at Distance 2 , 1992, SIAM J. Discret. Math..

[9]  W. K. Hale.  Frequency assignment: Theory and applications , 1980, Proceedings of the IEEE.

[10]  Madhumangal Pal,et al.  Fuzzy Planar Graphs , 2015, IEEE Transactions on Fuzzy Systems.

[11]  Pratima Panigrahi,et al.  On the Radio Number of Square of Graphs , 2015, Electron. Notes Discret. Math..

[12]  Pratima Panigrahi,et al.  On the radio number of toroidal grids , 2013, Australas. J Comb..

[13]  Lin Chen,et al.  Uncertain vertex coloring problem , 2019, Soft Comput..