Abstract
The distance two labelling and radio labelling problems are applicable to find the optimal frequency assignments on AM and FM radio stations. The distance two labelling, known as L(2,1)- labelling of a graph A, can be defined as a function, , from the vertex set V ( A ) to the set of all non-negative integers such that represents the distance between the vertices c and s in where the absolute values of the difference betweenand are greater than or equal to both 2 and 1 if = 1 and respectively. The L (2,1)- labelling number of , denoted by can be defined as the smallest number j such that there is an labeling with maximum label j . A radio labelling of a connected graph A is an injection k from the vertices of to such that , where represents the diameter of graph . The radio numbers of and A are represented by and which are the maximum number assigned to any vertex of and the minimum value of taken over all labellings k of , respectively. Our main goal is to obtain the bounds for the distance two labelling and radio labelling of nanostar tree dendrimers.
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