The bounds for the distance two labelling and radio labelling of nanostar tree dendrimer

Document Type

Article

Publication Date

1-1-2022

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, fc, from the vertex set V(A) to the set of all nonnegative integers such that d(c,s) represents the distance between the vertices c and 5 in A where the absolute values of the difference between k(c) and k(s) are greater than or equal to both 2 and 1 if d(c,s) = 1 and d(c,s) = 2, respectively. The L(2,1)-labelling number of A, denoted by λ2,l(A), can be defined as the smallest number j such that there is an L(2,1) —labeling with maximum label j. A radio labelling of a connected graph A is an injection k from the vertices of A to N such that (c,s) + |k(c) — k(s)l > 1 + d V c,s (Formula presented) V(A), where d represents the diameter of graph A. The radio numbers of fc and A are represented by rn(k) and rn(A) which are the maximum number assigned to any vertex of A and the minimum value of rn(k) taken over all labellings k of A, respectively. Our main goal is to obtain the bounds for the distance two labelling and radio labelling of nanostar tree dendrimers. © 2022. All Rights Reserved.

Keywords

Distance-two-labelling, Labelling, Radio labelling, Radio number

Publication Title

Telkomnika (Telecommunication Computing Electronics and Control)

Divisions

MathematicalSciences

Volume

20

Issue

1

Publisher

Universitas Ahmad Dahlan

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