Bounds for the Radio Number of Mesh Derived Architecture

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

“…The author studied in [18], [21] the same problem for the networks that contains the number of vertices in the n th dimension as 3𝑛 2 − 3𝑛 + 1 and 𝑛 2 , respectively. In addition, the authors in [14], [15], [17] studied the same problem for the graphs with 𝑛 vertices.…”

“…Bantva [19] slightly improved the lower bound that was established in [20]. In addition, Yenoke et al [21] proved that 𝑟 𝑛 (𝐸𝑁 (𝑛, 𝑛)) ≤ (𝑛 − 2)(4𝑛 2 − 9𝑛 + 8) + 2(𝑛 − 1) 2 + (𝑛 + 1), where 𝐸𝑁 (𝑛, 𝑛) is the enhanced mesh, 𝑛 ≥ 4. This paper is divided as follows:…”