On (a, d)-antimagic labelings of generalized Petersen graphs P(n, 5)

Abstract

A connected graph G = (V, E) is said to be (a, d)-antimagic if there exist positive integers a,d and a bijection f: E → {1,2,..., |E|} such that the induced mapping gf: V → N, denned by gf(v) = Σf(wv), uv ∈ E(G), is injective and gf{V) = {a,a + d,...,a + (|V| - l)d). Miller and Baca proved that the generalized Petersen graph P(n,2) is (3n+6/2,3)-antimagic for n = 0(mod 4),n ≥ 8 and conjectured that the generalized Petersen graph P(n, k) is (3n+6/2, 3)-antimagic for even n and 2 ≤ k ≤ n/2-1 and conjectured that the generalized Petersen graph P(n,k) is (5n+5/2, 2)-antimagic for odd n and 2 ≤ k ≤ n/2-1. Xu, Yang, Xi and Li proved that the generalized Petersen graph P(n, 3) is (3n+6/2, 3)-antimagic for n = 0(mod 4),n ≥ 8. In this paper, we show that the generalized Petersen graph P(n, 5) is (3n+6/2, 3)-antimagic for even n ≥ 12.