The generalized Petersen graph P(n, 7) is (3n+6/2,3)-antimagic

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, defined by gf(v) = Σ(uv), uv ∈ E(G), is bijective mapping and gf(V) = {a, a + d,..., a + (|V| - 1)d}. Mirka Miller and Martin Bača conjectured that the generalized Petersen graph P(n, k) is (3n+6/2, 3)-antimagic for even n and 2 ≤ k ≤ n/2-1. Xirong Xu et al., Wei Feng et al. proved that the generalized Petersen graph P(n, k) is (3n+6/2, 3)-antimagic for k = 3, k = 5 and even n, respectively. In this paper, we show that P(n, 7) is (3n+6/2, 3)-antimagic for even n ≥ 16.