Prime Labeling of Grids
نویسنده
چکیده
A labeling f on a graph G on n vertices is called a prime labeling if f is a bijection from the vertex set V (G) to {1, 2, · · · , n} such that f(x) and f(y) are coprime if x and y are adjacent. It was shown by Sundaram et al. [1] that the planar grid Pm × Pn has a prime labeling if m ≤ n and n is a prime. In this paper it is proved that the following grids have a prime labeling: (i) Pn+1 × Pn+1 has a prime labeling where n is an odd prime, n = 5 or n ≡ 3 or 9 (mod 10) and (n + 1) + 1 is also a prime. (ii) Pn × Pn+2 has a prime labeling where n is an odd prime and n ≡ 2 (mod 7).
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