Zeroth-order general Randić index of trees with given distance k-domination number
| Main Authors: | Vetrik, Tomas; Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa, Masre, Mesfin, Balachandran, Selvaraj |
|---|---|
| Other Authors: | National Research Foundation of South Africa |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2022
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1091 https://www.ejgta.org/index.php/ejgta/article/view/1091/pdf_217 |
Daftar Isi:
- The zeroth-order general Randić index of a graph G is defined as Ra(G)=∑v ∈ V(G)dGa(v), where a ∈ R, V(G) is the vertex set of G and dG(v) is the degree of a vertex v in G. We obtain bounds on the zeroth-order general Randić index for trees of given order and distance k-domination number, where k ≥ 1. Lower bounds are given for 0 < a < 1 and upper bounds are given for a < 0 and a > 1. All the extremal graphs are presented which means that our bounds are the best possible.