The bounds for the distance two labelling and radio labelling of nanostar tree dendrimer
| Main Authors: | Yenoke, Kins; Department of Mathematics, Loyola College, Chennai, India, Kaabar, Mohammed K. A.; Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, Malaysia |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
Universitas Ahmad Dahlan
, 2022
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| Subjects: | |
| Online Access: |
http://journal.uad.ac.id/index.php/TELKOMNIKA/article/view/20404 http://journal.uad.ac.id/index.php/TELKOMNIKA/article/view/20404/11170 |
Daftar Isi:
- 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, k, 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 s 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 λ2,1 (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 d(c, s) + |k(c) − k(s)| ≥ 1 + d ∀ c, s ∈ V(A), where d represents the diameter of graph A. The radio numbers of k 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.