<![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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