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
Divisions
MathematicalSciences
Publication Title
Telkomnika (Telecommunication Computing Electronics and Control)
Volume
20
Issue
1
Publisher
Universitas Ahmad Dahlan