<![CDATA[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 nonnegative integers such that ?(?, ?) represents the distance between the vertices c and s in ? where the absolute values of the difference between ?(?) and ?(?) are greater than or equal to both 2 and 1 if ?(?, ?)=1 and ?(?, ?) = 2, respectively. The L(2,1)-labelling number of ?, denoted by ?2,1 (?), can be defined as the smallest number j such that there is an ?(2,1) −labeling with maximum label j. A radio labelling of a connected graph A is an injection k from the vertices of ? to ? such that ?(?, ?) + |?(?) − ?(?)| ≥ 1 + ? ∀ ?, ? ∈ ?(?), 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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