Abstract

In this paper we will show applications of the Fibonacci numbers and the telephone numbers in edge coloured unicyclic graphs. In particular, we give the upper bound for the ( A , 2 B ) -index in unicyclic graphs. Moreover, we give characterization of the extremal graph achieving this maximum value. We also show connections between the number of ( A , 2 B ) -edge colourings in the class of unicyclic graphs and the telephone numbers as well as the Fibonacci numbers.

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